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	Differential geometry and topology - Wikipedia, the free encyclopedia
		Differential geometry is the study of geometry using calculus.
		Initially and up to the middle of the nineteenth century, differential geometry was studied from the extrinsic point of view: curves, surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions).
		Finsler geometry has the Finsler manifold as the main object of study — this is a differential manifold with a Finsler metric, i.e.
	en.wikipedia.org /wiki/Differential_geometry (1115 words)

	Differential geometry and topology Article, Differentialgeometryandtopology Information (Site not responding. Last check: 2007-10-20)
		Initially and up to the middle of the nineteenth century,differential geometry was studied from the extrinsic point of view: curves, surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions).
		The apparatus of differential geometry is that of calculus on manifolds: this includes the study of manifolds, tangent bundles, cotangent bundles, differential forms, exterior derivatives, integrals of p-forms over p-dimensional submanifolds and Stokes' theorem, wedgeproducts, and Lie derivatives.
		Finsler geometry has the Finsler manifold as the main object of study — this is a differential manifold with a Finsler metric, i.e.
	www.anoca.org /space/manifold/differential_geometry_and_topology.html (920 words)

	Finsler Geometry Is Just Riemannian Geometry without the Quadratic Restriction (Site not responding. Last check: 2007-10-20)
		The key idea in Finsler geometry is to consider the projectivized tangent bundle PTM (i.e., the bundle of line elements) of the manifold M. The main reason is that all geometric quantities constructed from F are homogeneous of degree zero in y and thus naturally live on PTM, even though F itself does not.
		The extension of the Gauss-Bonnet formula to Finsler geometry has been considered in [7], in which the relevant curvature forms were introduced and studied.
		As is well known, Riemannian geometry can be handled, elegantly and efficiently, by tensor analysis on M. Its handicap with Finsler geometry arises from the fact that the latter needs more than one space, for instance PTM in addition to M, on which tensor analysis does not fit well.
	www.math.iupui.edu /~zshen/Finsler/history/chern.html (2855 words)

	Finsler (Site not responding. Last check: 2007-10-20)
		Finsler' doctoral dissertation was supervised by Carathéodory on Curves and surfaces in general spaces.
		A Finsler space is a generalisation of a Riemannian space where the length function is defined differently and Minkowski's geometry holds locally.
		Finsler develops his approach to the paradoxes, his attitude towards formalised theories and his defence of Platonism in mathematics.
	www-history.mcs.st-andrews.ac.uk /history/Mathematicians/Finsler.html (522 words)

	The Finsler Geometry Newsletter - Home Page (Site not responding. Last check: 2007-10-20)
		The aim of the Newsletter is to promote the interaction between researchers in convex, integral, metric, and symplectic geometry by providing them with a quick, accessible medium for communicating ideas, announcements, examples, counter-examples, and remarks.
		The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations by Yan Yan Li and Louis Nirenberg.
		Finsler manifolds, manifolds whose tangent spaces carry a norm that varies smoothly with the base point, were born prematurely in 1854 together with the Riemannian counterparts in Riemann's ground-breaking
	www.math.poly.edu /research/finsler (264 words)

	Lectures on Finsler Geometry by Shen, Zhongmin (Site not responding. Last check: 2007-10-20)
		Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.
		Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view.
		The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.
	www.studentbookworld.com /BookDetail/9810245300.html (218 words)

	Differential geometry and topology at opensource encyclopedia (Site not responding. Last check: 2007-10-20)
		It is an analog of symplectic geometry which works for odd dimensional manifolds.
		Finsler geometry has Finsler manifold as the main object of study, it is a differential manifold with Finsler metric, i.e.
		Riemannian geometry has Riemannian manifold as the main object of study, its smooth manifolds with an additional structure which makes them look infinitesimally like Euclidean space and therefore allow to generalise the notion from Euclidean geometry such as gradient of a function, divergence, length of curves and so on.
	wiki.tatet.com /Differential_geometry.html (895 words)

	Finsler geometry in classical mechanics and in Bianchi cosmological models (Site not responding. Last check: 2007-10-20)
		The second example is particularly enlightening as the introduction of Finsler geometry overcomes the critical problems which cause the Jacobi (Riemannian) metric to fail.
		The Finsler geometrodynamical approach is particularly useful also because it gives a gauge-invariant characterization of chaos, which is always important, but becomes essential for General Relativistic dynamical systems.
		Finsler's geometry was developed by Berwald (1926), Eisenhart (1927), Knebelman (1929), Cartan (1934) and Rund (1959) [17].
	www.sif.it /cimento/tocb/112.02-03/06/06.html (3216 words)

	Finsler Geometry? Who ordered that? (Site not responding. Last check: 2007-10-20)
		Here I have some remarks on Finsler geometry: It is considered to be a generalization of Riemnannian geometry, on tangent bundles, with anisotropies of metric (depending on direction), which is more sophisticated and with less experimental evidence for such extensions.
		The conclusion is that we can not avoid Finsler geometry even in the usual (Einstein) gravity if the generic off-diagonal metrics and nonholonomic frames are considered.
		The main problem is that the bulk of monographs on Finsler geometry were written to emphasize more general constructions than the the Riemannian ones, just on tangent bundles.
	www.talkaboutscience.com /group/sci.astro/messages/489036.html (1510 words)

	A Sampler of Riemann-Finsler Geometry - Cambridge University Press
		Finsler geometry generalises Riemannian geometry in the same sense that Banach spaces generalise Hilbert spaces.
		Finsler geometry on complex vector bundles Tadashi Aikou; 4.
		Finsler geometry of holomorphic jet bundles Karen Chandler and Pit-Mann Wong; 5.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521831814 (266 words)

	PlanetMath: Finsler geometry
		So a natural geodesic distance can be defined on
		A finite dimensional Banach space is another simple example of Finsler space, where
		This is version 3 of Finsler geometry, born on 2005-02-18, modified 2005-06-06.
	planetmath.org /encyclopedia/FinslerGeometry.html (112 words)

	Amazon.ca: Books: Finsler Geometry: Joint Summer Research Conference on Finsler Geometry, July 16-20, 1995, Seattle, ... (Site not responding. Last check: 2007-10-20)
		Finsler Geometry: Joint Summer Research Conference on Finsler Geometry, July 16-20, 1995, Seattle, Washington
		A number of photos are featured in the volume, for example, that of Finsler.
		Top of Page : Finsler Geometry: Joint Summer Research Conference on Finsler Geometry, July 16-20, 1995, Seattle, Washington
	www.amazon.ca /exec/obidos/ASIN/082180507X (330 words)

	INTRODUCTION TO RIEMANN-FINSLER GEOMETRY by Bao, David, etc., D. BAO, UNIVERSITY OF HOUSTON, TX, USA; S.S. CHERN, ... (Site not responding. Last check: 2007-10-20)
		In Riemannian geometry, measurements are made with both yardsticks and protractors.
		In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms.
		Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature.
	www.studentbookworld.com /BookDetail/038798948X.html (208 words)

	Finsler geometry -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		Finsler geometry -- Facts, Info, and Encyclopedia article
		For each point x of M, and for every (A variable quantity that can be resolved into components) vector v in the (Click link for more info and facts about tangent space) tangent space T
		The length of γ, a (Click link for more info and facts about differentiable curve) differentiable curve in M is given by
	www.absoluteastronomy.com /encyclopedia/f/fi/finsler_geometry.htm (173 words)

	Finsler Geometry? Who ordered that? (Site not responding. Last check: 2007-10-20)
		N-connection from Finsler geometry and the diagonal terms are some
		The main problem is that the bulk of monographs on Finsler geometry were
		geometries that are far more fundamental than Riemannian geometries.
	www.groupsrv.com /science/about80500.html (1187 words)

	Transactions of the American Mathematical Society (Site not responding. Last check: 2007-10-20)
		It is known that the flag curvature of any projective Finsler metric is a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian).
		In this paper, we discuss the classification problem on projective Finsler metrics of constant flag curvature.
		P. Antonelli, R. Ingarden, and M. Matsumoto, The theory of sprays and Finsler spaces with applications in physics and biology, FTPH 58, Kluwer Academic Publishers, 1993.
	0-www.ams.org.library.uor.edu /tran/2003-355-04/S0002-9947-02-03216-6/home.html (588 words)

	Amazon.com: Lagrange and Finsler Geometry : Applications to Physics and Biology (Fundamental Theories of Physics): ... (Site not responding. Last check: 2007-10-20)
		The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian.
		Nevertheless, such geometries are playing an increasingly important role in a wide variety of problems in fields ranging from relativistic optics to ecology.
		Audience: This book is recommended as a (supplementary) text in graduate courses in differential geometry and its applications, and will also be of interest to physicists and mathematical biologists.
	www.amazon.com /exec/obidos/tg/detail/-/0792338731?v=glance (428 words)

	Shen, Zhongmin - Riemann-Finsler Geometry Books at Real Groovy New Zealand
		Note: items featured on this website may not be available in our stores.
		Curvature is the central concept in "Riemann-Finsler geometry".
		It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar flag curvature or isotropic S-curvature, etc. Instructive examples are given in abundance, for further description of some important geometric concepts.
	www.realgroovy.co.nz /books/isbn/9812383581 (457 words)

	Amazon.ca: Books: Handbook of Finsler Geometry (Site not responding. Last check: 2007-10-20)
		There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook.
		The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto.
		His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. ilasi (Spray and Finsler Geometry).
	www.amazon.ca /exec/obidos/ASIN/1402015577 (276 words)

	An Introduction to Riemann-Finsler Geometry (Graduate Texts in Mathematics) (D. Bao , S.-S. Chern , Z. Shen) (Site not responding. Last check: 2007-10-20)
		The authors claim to turn the subject of Finsler geometry with this book
		Finsler geometry are very well explained and the exercises
		which want to get a first aquaintance in Finsler geometry, find at least some help.
	www.interference.com /webstore/us/product/038798948X.htm (175 words)

	Table of contents for Library of Congress control number 2004057025 (Site not responding. Last check: 2007-10-20)
		Table of contents for A sample of Riemann-Finsler geometry / edited by David Bao...
		Volumes on normed and Finsler spaces J. Alverex Paiva and A. Thompson 2.
		Nonreversible Finsler metrics of positive flag curvature Hans-Bert Radenmacher 7.
	www.loc.gov /catdir/toc/cam051/2004057025.html (132 words)

	Proceedings of the American Mathematical Society
		The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.
		J.C. Álvarez Paiva and C. Durán, ``An Introduction to Finsler Geometry", Notas de la Escuela Venezolana de Matématicas, 1998.
		J.C. Álvarez Paiva, I.M. Gelfand, and M. Smirnov, Crofton densities, symplectic geometry, and Hilbert's fourth problem, in ``Arnold-Gelfand Mathematical Seminars, Geometry and Singularity Theory", V.I. Arnold, I.M. Gelfand, and V.S. Retakh (eds.), Birkhauser, Boston, 1997, pp.
	www.ams.org /proc/2001-129-08/S0002-9939-01-05910-X/home.html (259 words)

	Citations: The Differential Geometry of Finsler Spaces - Rund (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		Rund, The Differential Geometry of Finsler spaces, Springer, 1959.
		Minimal Entropy Rigidity For Finsler Manifolds Of Negative..
		A continuous function f : X Y is a morphism of timed HDA if and only if, i) for all n transition x 2 Xn, there exists a n transition y 2 Yn such that y = f ffi x.
	citeseer.ist.psu.edu /context/489404/0 (464 words)

	RIEMANN-FINSLER GEOMETRY
		Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics.
		Curvature is the central concept in Riemann—Finsler geometry.
		Readership: Graduate students and researchers in differential geometry.
	www.worldscibooks.com /mathematics/5263.html (150 words)

	Finsler Geometry Bao David/ Bao David Dai-wai/ Bao David D W / Chern Shiing-shen/ Shen Zhongmin- Textbook - Bookbyte.com
		Finsler Geometry Bao David/ Bao David Dai-wai/ Bao David D W / Chern Shiing-shen/ Shen Zhongmin- Textbook - Bookbyte.com
		Finsler Geometry by Bao, David/ Bao, David Dai-Wai/ Bao, David D.W./ Chern, Shiing-Shen/ Shen, Zhongmin
		Joint Summer Research Conference on Finsler Geometry, July 16-20, 1995, Seattle, Washington
	www.bookbyte.com /product.aspx?isbn=082180507X (132 words)

	Finsler Geometry - Reviewscout.com (Site not responding. Last check: 2007-10-20)
		Conference on Finsler Geometry, chaired by S. Chern and co-chaired by D. Bao
		Generalized Finsler metrics Applications to biology, engineering, and physics
		photographs are featured in the volumes, for example, that of Finsler.
	www.reviewscout.com /082180507X (234 words)

	Mathematics Archives - Topics in Mathematics - Differential Geometry
		Differential Geometry and Quantum Physics, SFB 288, TU Berlin
		GRTensor II Calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors.
		Lecture notes for the course in Differential Geometry
	archives.math.utk.edu /topics/differentialGeom.html (318 words)

	Lectures On Finsler Geometry; Author: Shen, Zhongmin; Paperback
		Lectures On Finsler Geometry; Author: Shen, Zhongmin; Paperback
		Viewing Finsler spaces as regular metric spaces, this work discusses the problems from the modern metric geometry point of view.
		It addresses the basics on Finsler spaces, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory.
	www.netstoreusa.com /mabooks/981/9810245319.shtml (180 words)

	Powell's Books - Fundamental Theories of Physics #12: Finsler Geometry, Relativity and Gauge Theories by G. S. Asanov
		Powell's Books - Fundamental Theories of Physics #12: Finsler Geometry, Relativity and Gauge Theories by G. Asanov
		The Geometry of Higher-Order Hamilton Spaces: Applications to Hamiltonian Mechanics
		Fundamental Theories of Physics #12: Finsler Geometry, Relativity and Gauge Theories
	www.powells.com /cgi-bin/biblio?inkey=61-9027719608-1 (376 words)

	Streaming Video - Spring 2002
		Panayiotis Charalambos Stavrinos: Remarks on the Applications of Finsler Geometry to Space-Time
		Robert L. Bryant: The Generality of Finsler Metrics of Constant Flag Curvature and some Exotic Holonomy Groups
		Ralph Beil: Finsler Geometry and Relativistic Field Theory
	www.msri.org /publications/video/index04.html (1274 words)

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