Lectures On Closed Geodesics
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Lectures On Closed Geodesics
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Author : W. Klingenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Closed Geodesics written by W. Klingenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres ponding periodic orbit in the geodesic flow is infinitesimally stable.
Lectures On Closed Geodesics
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Author : Wilhelm Klingenberg
language : en
Publisher: Springer
Release Date : 1978
Lectures On Closed Geodesics written by Wilhelm Klingenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Curves on surfaces categories.
Lectures On Closed Geodesics
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Author : W. Klingenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 1978-01-01
Lectures On Closed Geodesics written by W. Klingenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01-01 with Mathematics categories.
The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres ponding periodic orbit in the geodesic flow is infinitesimally stable.
Closed Geodesics On Riemannian Manifolds
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Author : Wilhelm Klingenberg (Mathématicien)
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Closed Geodesics On Riemannian Manifolds written by Wilhelm Klingenberg (Mathématicien) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Contains expository lectures from the CBMS Regional Conference held at the University of Florida, 1982. This book considers a space formed by various closed curves in which the closed geodesics are characterized as the critical points of a functional, an idea going back to Morse.
Lectures On Geodesics In Riemannian Geometry
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Author : Marcel Berger
language : en
Publisher:
Release Date : 1965
Lectures On Geodesics In Riemannian Geometry written by Marcel Berger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Geodesics (Mathematics). categories.
Tsing Hua Lectures On Geometry Analysis
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Author : Shing-Tung Yau
language : en
Publisher: International Press of Boston
Release Date : 1997
Tsing Hua Lectures On Geometry Analysis written by Shing-Tung Yau and has been published by International Press of Boston this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
A collection of lectures given by the author and numerous contributors at Tsing Hua University, Taiwan, in 1990-1. Topics covered include: energy in general relativity; existence and convergence of solutions; closed geodesics; and mean curvature evolution.
On The Geometry Of Simple Closed Geodesics
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Author : Hugo Parlier
language : en
Publisher:
Release Date : 2004
On The Geometry Of Simple Closed Geodesics written by Hugo Parlier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Lectures On Finsler Geometry
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Author : Zhongmin Shen
language : en
Publisher: World Scientific
Release Date : 2001
Lectures On Finsler Geometry written by Zhongmin Shen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. 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.
Closed Geodesics On Complete Surfaces
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Author : Victor Bangert
language : de
Publisher:
Release Date : 1979
Closed Geodesics On Complete Surfaces written by Victor Bangert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
One Sided Closed Geodesics On Surfaces
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Author : Joel Hass
language : en
Publisher:
Release Date : 1984
One Sided Closed Geodesics On Surfaces written by Joel Hass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Geodesics (Mathematics) categories.