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Topic: Contact geometry

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	contact lenses
		The Reverse Geometry OK® Contact Lens for Orthokeratology rigid gas-permeable contact lens, made by ConTEX, Sherman Oaks, Calif., is the first contact lens designed to correct nearsightedness by temporarily reshaping the transparent tissue known as the cornea that covers the iris and pupil.
		Under the binding down of a rigid contact lens during sleep, the flow of tears and oxygen to the cornea is further reduced.
		Daily-wear contact lenses are removed daily for cleaning and are a safer choice, provided they aren't worn during sleep.
	www.caridon.com /contact-lenses.html (742 words)

	Contact geometry - Wikipedia, the free encyclopedia
		In mathematics, contact geometry is the study of completely nonintegrable hyperplane fields on manifolds.
		One difference between contact and symplectic geometry is that every 3-manifold admits a contact structure while there are cohomological obstructions to the existence of symplectic structures.
		Contact geometry also has applications to low-dimensional topology; for example, it has been used by Kronheimer and Mrowka to prove the property P conjecture and by Gompf to derive a topological characterization of Stein manifolds.
	en.wikipedia.org /wiki/Contact_geometry (768 words)

	Technical Tips for Surface-to-Surface Contact Analysis in MES (Site not responding. Last check: 2007-10-16)
		Contact pairs can be defined either by selecting two surfaces on the model, right-clicking and choosing "Surface-to-Surface Contact", or by right-clicking in the graphics area (with nothing selected), choosing "General Surface-to-Surface Contact" and manually filling in the Contact Pairs spreadsheet.
		When contact surfaces undergo large displacement or large deformation such as more than 50% strain even in the localized area, the basic assumption used in calculating contact parameters, such as master and target surfaces, contact type and contact extend area, may no longer be valid.
		Considering the initial geometry, point-to-surface contact appears to be a proper choice because the segments on the master surface are much larger than the segments on the target surface.
	www.algor.com /news_pub/tech_white_papers/surface_contact/default.asp (4423 words)

	How Probe Tip Geometry Affects Contact Reliability
		A chisel contacting the rim of an open via is a special case (a chisel is essentially a pyramid with a triangular base).
		The area of contact is easy to envision - it is spread over three regions which are the points of contact between the rim of the hole and the three ridges formed by the intersections of the chisel faces.
		This is because the reaction force is perpendicular to the attack angle of the ridge and increases geometrically as a function of this angle.
	www.qatech.com /tech/applications_notes/AN02.htm (953 words)

	PlanetMath: contact manifold
		A co-oriented contact structure is a subbundle of
		is a contact manifold with the contact structure induced by the one form
		This is version 1 of contact manifold, born on 2003-06-27.
	planetmath.org /encyclopedia/ContactManifold.html (107 words)

	Amazon.com: Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications): ... (Site not responding. Last check: 2007-10-16)
		Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software.
		Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied.
		Contact Geometry and Linear Differential Equations by Vladimir E. Nazaikinskii
	www.amazon.com /Nonlinear-Differential-Encyclopedia-Mathematics-Applications/dp/0521824761 (835 words)

	Astrology on the Web: Sacred Geometry in Armenia
		If you can bear to remember your geometry classes, you will find that the origins of mathematics and how it was used by the ancients to construct their cities and temples has not changed that much over time, it has just become more complex (and has fueled the success of hand calculators).
		Exactly where geometry came from we are not sure, but the source has moved a little East of where people used to think it came from.
		For without geometry, you cannot build anything, and its knowledge was key to survival, and believed to be a key to unlocking the secrets of the universe.
	www.astrologycom.com /geometry.html (1377 words)

	Differential Geometry (Site not responding. Last check: 2007-10-16)
		Differential geometry is the study of geometry using calculus.
		As its sister, symplectic geometry, belongs to the even-dimensional world, contact geometry is the odd-dimensional counterpart.
		Finsler geometry has the Finsler manifold as the main object of study — this is a differential manifold with a Finsler metric, i.e.
	www.differentialgeometry.net (213 words)

	Symplectic and Contact Geometry - Summer Tutorial 2003
		Contact manifolds are the odd-dimensional analogues of symplectic manifolds, and they appear naturally when one is interested in symplectic structures on manifolds with boundary.
		Two important results that we will prove are: Darboux's theorem on the local triviality of symplectic and contact manifolds, and Martinet's theorem that every closed orientable 3-manifold admits a contact structure.
		H. Geiges, "Contact geometry," in Handbook of Differential geometry vol.
	www.math.princeton.edu /~cmanoles/symcon.html (529 words)

	Etnyre: Contact Geometry Class (Site not responding. Last check: 2007-10-16)
		Contact geometry was born more than two centuries ago in the work of Huygens, Hamilton, Jacobi as a geometric language for optics.
		One encounters contact geometry in everyday life when parking a car, skating, using a refrigerator, or watching the beautiful play of light in a glass of water.
		With the birth of symplectic and contact topology in the Eighties, the subject was reborn, and the last decade witnessed a number of breakthrough discoveries.
	www.math.gatech.edu /~etnyre/class/Contact03/index.html (237 words)

	Contact reading (Site not responding. Last check: 2007-10-16)
		Etnyre "Symplectic convexity in low-dimensional topology" Symplectic, contact and low-dimensional topology (Athens, GA, 1996).
		Hofer and M Kriener, "Holomorphic curves in contact dynamics," to appear in the proceedings of a conference on the occasion of the 70th birthday of P. Lax and L. Nirenberg
		There is a very promising connection between foliation theory and contact geometry that has only begun to be pursued.
	math.stanford.edu /contact/reading.html (515 words)

	Stanford Symplectic Geometry Seminar 2004-2005
		It turns out that the corresponding results in contact geometry exhibit a quantum behavior: there are non-squeezing results for domain of size larger than $\hbar$ but not for small ones.
		Abstract: Tropical varieties are limit objects of the so-called amoebas of complex algebraic varieties under a certain deformation of the ambient complex structure.
		Abstract: Contact homology is a powerful invariant for contact structures, and can be thought of as an infinite dimensional Morse theory for the action functional.
	math.stanford.edu /~lipshitz/seminar0405 (2052 words)

	ARCC Workshop: Holomorphic curves in contact geometry (Site not responding. Last check: 2007-10-16)
		This workshop, sponsored by AIM and the NSF, will be devoted to the development of holomorphic curve techniques in contact geometry and topology.
		The advent of holomorphic curve techniques in contact topology, as exemplified in Symplectic Field Theory (SFT), and asymptotically holomorphic curve techniques, in the spirit of Donaldson, has allowed one to use a diverse set of geometric, analytic and topological tools when studying contact structures.
		The workshop will bring together researchers in contact and symplectic geometry, dynamics, low-dimensional topology and physics, who will explore connections between the various approaches people have taken to using holomorphic curves, develop new holomorphic curve techniques and apply them to various questions in contact and symplectic geometry and low-dimensional topology.
	www.aimath.org /ARCC/workshops/contactgeom2.html (325 words)

	Contact Naked Geometry
		Use the form below to send a note or idea -- we'd love to hear from you.
		Naked Geometry showcases exquisite geometric ideas and forms using the human body as the medium.
		Naked Geometry is for those who love beautiful expressions of the mind, spirit, and body.
	www.nakedgeometry.com /contact.html (85 words)

	53: Differential geometry
		Differential geometry is the language of modern physics as well as an area of mathematical delight.
		Geometry of spheres is in the sphere FAQ.
		A metric in the sense of differential geometry is only loosely related to the idea of a metric on a metric space.
	www.math.niu.edu /~rusin/known-math/index/53-XX.html (461 words)

	The Online Course Network
		This geometry course is designed for those students, young or old, who need a thorough course in Geometry.
		A particular geometry textbook is required for the course.
		You will need to contact me for the ISBN number to be assured of purchasing the correct book.
	www.onlinecourse.com /courses/syllabus/geometry.htm (697 words)

	Contact and Symplectic Geometry - Cambridge University Press
		3-dimensional contact geometry C. Thomas (based on lectures by Y. Eliashberg and E. Giroux); 4.
		Topology and analysis of contact circles H. Geiges and J. Gonzalo; 5.
		On closed trajectories of a charge moving in a magnetic field - an application of symplectic geometry V. Ginzburg; 7.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521570867 (363 words)

	Augustin Banyaga - Mathematician of the African Diaspora
		Geometry, topology, and dynamics (Montreal, PQ, 1995), 1--15, CRM Proc.
		Banyaga, Augustin Invariants of contact structures and transversally oriented foliations.
		Differential geometry: geometry in mathematical physics and related topics (Los Angeles, CA, 1990), 9--17, Proc.
	www.math.buffalo.edu /mad/PEEPS/banyaga_augustin.html (1021 words)

	[No title]
		My longtime interest has been in the study of the algebra, the geometry, the topology and the dynamics of symplectic, contact, volume preserving, and measure preseving diffeomorphisms of smooth manifolds.
		This is an integrated and uniform formulation of the generalization to contact geometry of the classical Arnold-Liouville theorem, Duistermaat theory of Lagrangian fibrations, the famous Atiyah-Guillen-Sternberg convexity theorem for the moment map, and Delzant realization theorem.
		On the other hands, this leads to an interest in the geometry of gauge fields, especially the study of the structure of symplectic diffeomorphisms of the moduli space of flat connections on S0(3) bundles over surfaces.
	www.math.psu.edu /banyaga/vita.html (2038 words)

	Robotics Institute: Motion Constraints from Contact Geometry: Representation and Analysis (Site not responding. Last check: 2007-10-16)
		A method to determine constraints on translational and rotational motion of planar and 3-D objects from their contact geometry is presented.
		Subspaces in M/sub a/ that represent the range of values of motion parameters that are disallowed due to the contact are identified.
		Khosla, "Motion Constraints from Contact Geometry: Representation and Analysis," Proc.
	www.ri.cmu.edu /pubs/pub_2312_text.html (280 words)

	[No title]
		Geometry and Physics of G2 Manifolds, April 29 - May 2, 2003
		Symplectic geometry originated as a mathematical outgrowth of Hamiltonian mechanics and dynamical systems and their applications to the theory of elementary particles, oceanographic and atmospheric sciences, condensed matter, accelerator and plasma physics and other disciplines at the classical and quantum levels.
		Ideally, a good mathematical model for the very complex systems listed above should describe the global information regarding the phase structure by means of relevant parameters rather than describing the existence of a specific solution of the equations of motion.
	www.ipam.ucla.edu /programs/sgp2003 (447 words)

	Richard E. Phillips Lecture Series 2006
		An attempt to find an analog of this result in contact geometry brings a surprising answer: while contact non-squeezing phenomenon exists on large scales, it disappears on small scales.
		It turns out that the contact (non-)squeezing problem is tightly related to the problem of existence of a natural partial order on the universal cover of the contactomorphisms group of a contact manifold.
		On the other hand, Stein manifolds have a canonical built-in symplectic geometry, which is essential for understanding their complex geometry.
	www.mth.msu.edu /Lecture_Series/2006.html (398 words)

	contact - OneLook Dictionary Search
		Contact : Online Plain Text English Dictionary [home, info]
		Phrases that include contact: contact print, contact dermatitis, contact inhibition, eye contact, contact language, more...
		Words similar to contact: reach, contacted, contacting, impinging, liaison, link, middleman, striking, tangency, touch, get hold of, get through, getto, inter-group communication, more...
	www.onelook.com /?w=contact (481 words)

	Graduate Student Seminar
		If time permits, I will outline some deeper connections between the contact geometry and the topology of the underlying manifolds.
		This seemingly simple question in elementary geometry generated a lot of interest earlier this century.
		It was known that a 33 x 32 rectangle could be tiled, as well as a 177 x 176 rectangle.
	people.brandeis.edu /~rtorrey/gss.html (926 words)

	Contact cat yronwode
		Due to the number of people who try to contact me, i regret to say that i do not have time to perform consultations by email at all any more.
		This is the most reliable forum through which i may be contacted on the subject, as i am unable to respond to email otherwise due to the duties of my regular work and the sheer number of requests i receive for personal correspondence.
		If you wish to contact me about arranging for special use of my label art (as was done when my labels appeared on the cover and in the booklet of a blues CD by a British guitarist), please drop a note to
	www.luckymojo.com /contact.html (3294 words)

	Geometry Advice online - Contact Geometry Experts - LIVE at Kasamba.com! (Site not responding. Last check: 2007-10-16)
		Recommend the Geometry category to a friend or colleague
		B Tech expert In solving any type of GEOMETRY Problem with full details and accuracy with exp of last 10yrs
		Use of this website constitutes acceptance of the Kasamba Terms of Service and Privacy Policy.
	www.kasamba.com /experts/education-tutoring/math/geometry (254 words)

	Stock Market Geometry - Email Contact Form
		Please use this convenient email contact form to send us your comments and questions about the products on this website.
		Cowan is often out of the country conducting private research in areas where email is unavailable, inquiries submitted here may not be immediately answered.
		Cowan does not provide market advise or tutelage and none will be provided by submitting a request in the below form.
	www.cycle-trader.com /contact.htm (83 words)

	Timken - Bearings - Engineering - Intro - Contact Geometry
		: bearings : engineering : intro : contact geometry
		Standard tapered roller bearings have components with profiles which result in uniform stress distribution under normalloading conditions along the effective roller contact length (fig.
		For extremely heavy loads or significant misalign-ment, or both, modified profiles can be provided to minimise geometric stress concentration at the ends of roller contact.
	www.timken.com /products/bearings/engineer/contact.asp (79 words)

	Proceedings of the American Mathematical Society
		Abstract: In this paper, we give an open book decomposition for the contact structures on some Brieskorn manifolds, in particular for the contact structures of Ustilovsky.
		H. Geiges, Contact geometry, to appear in the Handbook of Differential Geometry, vol.
		E. Giroux, Géométrie de contact: de la dimension trois vers les dimensions supérieures, Proceedings of the International Congress of Mathematicians, Vol.
	www.ams.org /proc/2005-133-12/S0002-9939-05-07944-X/home.html (211 words)

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