
	Where results make sense

Topic: Submanifolds

	PlanetMath: examples of Lagrangian submanifolds
		is a Lagrangian submanifold of the cotangent bundle
		Cross-references: structure, canonical, cotangent bundle, Lagrangian submanifold, smooth function, manifold
		This is version 3 of examples of Lagrangian submanifolds, born on 2005-05-22, modified 2006-09-20.
	planetmath.org /encyclopedia/ExamplesOfLagrangianSubmanifolds.html (76 words)

	Colloquium Talks (Site not responding. Last check: 2007-10-20)
		The new classes of submanifolds: (k,ε)-saddle, (kε)-parabolic, (k,ε)-asymptotic and (k,ε)-convex are defined in terms of eigenvalues of their 2-nd fundamental form.
		The dimension of asymptotic subspaces and the index of relative nullity of submanifolds with non-positive extrinsic (sectional, q-th Ricci, q-th scalar) curvature are estimated from below.
		The characterizations of totally geodesic submanifolds and cylinders and extremal theorem for Riemannian spaces of positive curvature are obtained.
	math.haifa.ac.il /TOUFIK/colloquium/colloquium.html (2382 words)

	Submanifolds books, find the lowest prices (Site not responding. Last check: 2007-10-20)
		Tight and Taut Submanifolds : Papers in Memory of Nicolaas H. Kuiper
		Differential Geometry of Submanifolds : Proceedings of the Conference Held a Kyoto, January 23-25, 1984
		Total Mean Curvature and Submanifolds of Finite Type
	www.allbookstores.com /Submanifolds.html (129 words)

	CVGMT: Measure of non-horizontal submanifolds (Site not responding. Last check: 2007-10-20)
		k)-dimensional spherical Hausdorff measure of a k-codimensional submanifold with respect to its Riemannian measure.
		These results stem from a blow-up theorem at non-horizontal points, where we rescale the submanifold with respect to group dilations and we show its convergence to a subgroup with respect to the Hausdorff convergence of sets.
		We extend this blow-up to horizontal points of submanifolds in two step stratified groups.
	cvgmt.sns.it /papers/mag05a (145 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Structure results are proved for submanifolds of Euclidean spaces with semiparallel Ricci tensor under certain additional conditions.
		A geometric description of a class of normally flat semi-Einstein submanifolds with multiple principal curvature vectors is presented.
		V A Mirzoyan, "Structure theorems for Ricci-semisymmetric submanifolds and geometric description of a class of minimal semi-Einstein submanifolds", SB MATH, 2006, 197 (7), 997-1024.
	www.turpion.org /php/paper.phtml?journal_id=sm&paper_id=3786 (82 words)

	DC MetaData for: Genuine deformations of submanifolds (Site not responding. Last check: 2007-10-20)
		Since a submanifold of a deformable one is also deformable, to go deeper into the isometric deformation problem for submanifolds one has to discard those deformations that arise this way.
		First, to introduce the concept of genuine deformation, and then to give the (quite restricted) geometric structure of the submanifolds that admit deformations of this kind.
		The unifying character and geometric nature, as opposed to a purely algebraic one, of our main result suggest that it should be the starting point for a deformation theory extending the classical one for hypersurfaces to higher codimension.
	www.preprint.impa.br /Shadows/SERIE_A/2001/105.html (139 words)

	Surfaces, submanifolds, and aligned fox reimbedding in non-Haken 3-manifolds
		We describe some results for closed orientable surfaces in non-Haken manifolds, and extend Fox's theorem for submanifolds of the 3-sphere to submanifolds of general non-Haken manifolds.
		In the case where the submanifold has connected boundary, we show also that the partial derivative-connected sum decomposition of the submanifold can be aligned with such a structure on the submanifold's complement.
		M Scharlemann and A Thompson, "Surfaces, submanifolds, and aligned fox reimbedding in non-Haken 3-manifolds" (2005).
	repositories.cdlib.org /postprints/953 (152 words)

	UC Davis Math: Colloquia and Seminars
		The purpose of this talk is to relate the geometries of calibrated submanifolds to their gauge theories.
		We study the moduli space of deformations of a special kind of associative submanifolds in a $G_2$ manifold (which we call complex associative submanifolds); and we study the moduli space of deformations of a special kind of Cayley submanifolds (which we call complex Cayley submanifolds).
		We propose a certain counting invariant for associative and Cayley submanifolds of foliated manifolds.
	www.math.ucdavis.edu /research/seminars/?type=5&when=past&talkid=1109 (113 words)

	DC MetaData for: Reducibility of Dupin submanifolds (Site not responding. Last check: 2007-10-20)
		This problem is important on its own right in the theory of submanifolds in space forms, and it is completely solved in the paper.
		This observation can be seen as a generalization of the classical fact that the orthogonal surfaces of a cyclic system are Ribaucour transforms one of each other.
		One of the main results of this paper is that any submanifold that carries a Dupin principal normal with integrable conullity arises locally this way.
	www.preprint.impa.br /Shadows/SERIE_A/2001/103.html (270 words)

	07w5059 Minimal submanifolds and related problems (Site not responding. Last check: 2007-10-20)
		A 5-day workshop in the summer of 2007 at BIRS on "Minimal submanifolds and related problems" is needed to stimulate the classical yet also modern mathematical field of minimal submanifolds.
		Calibrated geometry, a subfield of minimal submanifolds, also witnessed a new wave of insights.
		The partial differential equations which govern calibrated minimal submanifolds, such as the special Lagrangian equations, are usually fully nonlinear ones.
	www.pims.math.ca /birs/birspages.php?task=displayevent&event_id=07w5059 (251 words)

	PUBLICATIONS (still under construction, please check back later)
		Here we prove that the moduli space of coassociative deformations of an asymptotically cylindrical coassociative submanifold C asymptotic to L_s x (R,infty), for s in F, is a smooth manifold of dimension equal to dim (V_+)+dim(ker(Phi))=dim (V_+)+b^2(L)-b^0(L)+b^3(C)-b^1(C)+b^0(C).
		Abstract: The purpose of this paper is to relate the geometries of calibrated submanifolds to their gauge theories.
		We discuss the relation to Seiberg-Witten theory, and propose a certain counting invariant for associative and Cayley submanifolds of foliated manifolds.
	www.math.northwestern.edu /~salur/preprint.html (535 words)

	Table of contents for Library of Congress control number 2003041924
		143 5.3 Geometric properties of submanifolds with constant principal curva- tures.
		174 6 Rank rigidity of submanifolds and normal holonomy of orbits 177 6.1 Submanifolds with curvature normals of constant length and rank of homogeneous submanifolds.....................
		219 8 Submanifolds of Riemannian manifolds 223 8.1 Submanifolds and the fundamental equations............
	www.loc.gov /catdir/toc/fy038/2003041924.html (259 words)

	Research Interests
		For example they are (i) holomorphic curves and Lagrangian submanifolds in symplectic manifolds and (ii) associative submanifolds and coassociative submanifolds in G₂-manifolds.
		We explain the correspondence between coisotropic submanifolds in M and Lagrangians in the symplectic knot space.
		For each submanifold X in a sphere Sⁿ, we show that the corresponding conormal bundle N^{}X is Lagrangian for the Stenzel form on T^{}Sⁿ.
	www.math.wustl.edu /~jhlee/Connect2.htm (867 words)

	MERL – TR2004-134 – From Subspaces to Submanifolds
		MERL – TR2004-134 – From Subspaces to Submanifolds
		This paper identifies a broad class of nonlinear dimensionality reduced (NLDR) problems where the exact local isometry between an extrinsically curved data manifold M and a low-dimensional parameterization space can be recovered from a finite set of high-dimensional point sampels.
		We show how to use the GNA operator for denosing, dimensionality reduction, and resynthesis of both the original data and of new samples, making such "submanifold" methods an attractive alternative to subspace methods in data analysis.
	www.merl.com /publications/TR2004-134 (182 words)

	Baouendi, M.S., Ebenfelt, P., Rothschild, L.P.: Real Submanifolds in Complex Space and Their Mappings.
		This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students.
		One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds.
		The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions.
	press.princeton.edu /titles/6663.html (294 words)

	On the nonexistence of stable currents in submanifolds of a Euclidean space, Xueshan Zhang
		In this paper, we regard $M^m$ as a submanifold immersed in a Euclidean space and prove the conjecture under some pinched conditions about the sectional curvatures and the principal curvatures of $M^m$.
		We also show that there is no stable $p$-current in a submanifold of $M^m$ and the $p$-th homology group vanishes when the shape operator of the submanifold satisfies certain conditions.
		R. Howard, The nonexistence of stable submanifolds, varifolds, and harmonic maps in sufficiently pinched simply connected Riemannian manifolds, Michigan Math.
	projecteuclid.org /getRecord?id=euclid.tmj/1113246746 (289 words)

	Transactions of the American Mathematical Society
		Then we consider 3-dimensional totally real submanifolds which are linearly full in
		R.L. Bryant, Submanifolds and special structures on the octonians, J. Differential Geom.
		K. Sekigawa, Almost complex submanifolds of a 6-dimensional sphere, K\={o}dai Math.
	www.ams.org /tran/1996-348-04/S0002-9947-96-01626-1/home.html (461 words)

	[No title]
		For example, conjecturally special lagrangian submanifolds play a central role in understanding the structure of Calabi-Yau 3-folds and in mirror symmetry (Strominger-Yau-Zaslow).
		Recently geometric flow techniques, in particular, mean curvature flow, have been applied to lagrangian submanifolds (Thomas-Yau, M-T Wang) to construct special lagrangians in special cases.
		Mean curvature flow, and its possible application to the construction of special lagrangian submanifolds.
	www.ipam.ucla.edu /programs/gls2003 (288 words)

	CJM - Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices
		An explicit calculation for the minimal distance function from the geodesic submanifold mathrm{Sym}(p,{mathbb R})
		We explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold mathrm{Sym}(n,{Bbb R})
		Matrix approximation, positive, definite matrix, geodesic submanifold, Cartan-Hadamard manifold, best approximation, minimal distance function, global tubular, neighborhood theorem, Schur complement, metric and spectral, geometric mean, Cayley transform
	www.journals.cms.math.ca /cgi-bin/vault/view/lim2233 (165 words)

	İnönü Üniversitesi
		Sahin,Bayram QR-lightlike submanifolds of indefinite quaternion Kaehler manifold.
		Sahin,Bayram A theorem on complex submanifolds of a complex projective space.
		Krishan L. Duggal and Bayram Şahin Generalized CR-lightlike submanifolds of Kaehler manifolds Acta Math.
	www.inonu.edu.tr /personel/personel.php?email=bsahin&secim=yayin (474 words)

	CRC Press Online (Site not responding. Last check: 2007-10-20)
		Applies the tool of normal holonomy to the study of isoparametric submanifolds and their focal manifolds, orbits of linear Lie group actions and homogeneous submanifolds, and homogeneous structures on submanifolds
		With special emphasis on new techniques based on the holonomy of the normal connection, this book provides an up-to-date, complete introduction to submanifold geometry.
		It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers.
	www.crcpress.com /shopping_cart/products/product_detail.asp?sku=C3715&parent_id=&pc= (319 words)

	$1$-type submanifolds of the complex projective space, Ivko Dimitrić
		[1] CECIL, T., Geometric applications of critical point theory to submanifolds of com-plex projective space, Nagoya Math.
		[3] CHEN, B. Y., Total Mean Curvature and Submanifolds of Finite Type, Worl Scientific, Singapore 1984.
		[11] Ros, A., On spectral geometry of Kaehler submanifolds, J. Math.
	projecteuclid.org /getRecord?id=euclid.kmj/1138039399 (242 words)

	MINIMAL SUBMANIFOLDS AND RELATED TOPICS
		Chapter 1.4: Minimal Submanifolds in the Sphere (136k)
		The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds.
		The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
	www.worldscibooks.com /mathematics/5417.html (112 words)

	World Scientific
		Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile.
		He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.
		Inspired by Chern and his work, former colleagues, students and friends - themselves highly regarded mathematicians in their own right - come together to honor and celebrate Chern's huge contributions.
	www.wspc.com.sg (480 words)

	DC MetaData for: Hermitian and Kähler Submanifolds of a Quaternionic Kähler Manifold (Site not responding. Last check: 2007-10-20)
		DC MetaData for: Hermitian and Kähler Submanifolds of a Quaternionic Kähler Manifold
		when such submanifold is Hermitian, almost K\"ahler and K\"ahler.
		Keywords: Quaternion Kahler manifold, almost Hermitian submanifold, Kahler submanifold, parallel submanifold
	www.esi.ac.at /Preprint-shadows/esi827.html (112 words)

	Wiqing Gu at MSRI - Examples of Associative, Co-associative and Cayley Submanifolds (Site not responding. Last check: 2007-10-20)
		Wiqing Gu at MSRI - Examples of Associative, Co-associative and Cayley Submanifolds
		Wiqing Gu - Examples of Associative, Co-associative and Cayley Submanifolds
		A PDF version of the lecture notes is available here.
	www.msri.org /publications/ln/msri/2003/vonneumann/gu/1/index.html (32 words)

Try your search on: Qwika (all wikis)