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黎曼-芬斯勒幾何導論 版權信息
- ISBN：9787510005053
- 條形碼：9787510005053 ; 978-7-5100-0505-3
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
黎曼-芬斯勒幾何導論 本書特色
《黎曼:芬斯勒幾何導論(英文版)》是由世界圖書出版公司出版的。
黎曼-芬斯勒幾何導論 內容簡介
This book project began as an attempt to sort through the literature on Finsler geometry. It was our intention to write a systematic account about that part of the material which is both elementary and indispensable. We want to thank many fellow geometers for their encouragement, for answering our email calls for help, and for steering us towards the pertinent references. Some of these colleagues also helped us by proof-reading parts of the manuscript.
黎曼-芬斯勒幾何導論 目錄
preface
acknowledgments
part one finsler manifolds and their curvature
chapter 1 finsler manifolds and the fundamentals of minkowski norms
1.0 physical motivations
1.1 finsler structures: definitions and conventions
1.2 two basic properties of minkowski norms
1.2 a. euler's theorem !,
1.2 b. a fundamental inequality
1.2 c. interpretations of the fundamental inequality
1.3 explicit examples of finsler manifolds
1.3 a. minkowski and locally minkowski spaces
1.3 b. riemannian manifolds
1.3 c. randers spaces
1.3 d. berwald spaces
1.3 e. finsler spaces of constant flag curvature
1.4 the fundamental tensor and the cartan tensor
references for chapter 1
chapter 2 the chern connection
2.0 prologue
2.1 the vector bundle tm and related objects
2.2 coordinate bases versus special orthonormal bases
2.3 the nonlinear connection on the manifold tm
2.4 the chern connection on tm
2.5 index gymnastics
references for chapter 2
chapter 3 curvature and schur's lemma
3.1 conventions and the hh-, hv-, w-curvatures
3.2 first bianchi identities from torsion freeness
3.3 formulas for r and p in natural coordinates
3.4 first bianchi identities from "almost" g-compatibility
3.5 second bianchi identities
3.6 interchange formulas or ricci identities
3.7 lie brackets among the and the
3.8 derivatives of the geodesic spray coefficients gi
3.9 the flag curvature
3.10 schur's lemma
references for chapter 3
chapter 4 finsler surfaces and a generalized gauss-bonnet theorem
4.0 prologue
4.1 minkowski planes and a useful basis
4.2 the equivalence problem for minkowski planes
4.3 the berwald frame and our geometrical setup on sm
4.4 the chern connection and the invariants i, j, k
4.5 the riemannian arc length of the indicatrix
4.6 a gauss-bonnet theorem for landsberg surfaces
references for chapter 4
part two calculus of variations and comparison theorems
chapter 5 variations of arc length,
chapter 6 the gauss lemma and the hopf-rinow theorem
chapter 7 the index form and the bonnet-myers theorem
chapter 8 the cut and conjugate loci, and synge's theorem
chapter 9 the cartan-hadamard theorem and rauch's first theorem
part three special finsler spaces over the reals
chapter 10 berwald spaces and szab6's theorem for berwald surfaces
chapter 11 randers spaces and an elegant theorem
chapter 12 constant flag curvature spaces and akbar-zadeh's theorem
chapter 13 riemannian manifolds and two of hopf's theorems
chapter 14 minkowski spaces, the theorems of deicke and brickell bibliography
index
acknowledgments
part one finsler manifolds and their curvature
chapter 1 finsler manifolds and the fundamentals of minkowski norms
1.0 physical motivations
1.1 finsler structures: definitions and conventions
1.2 two basic properties of minkowski norms
1.2 a. euler's theorem !,
1.2 b. a fundamental inequality
1.2 c. interpretations of the fundamental inequality
1.3 explicit examples of finsler manifolds
1.3 a. minkowski and locally minkowski spaces
1.3 b. riemannian manifolds
1.3 c. randers spaces
1.3 d. berwald spaces
1.3 e. finsler spaces of constant flag curvature
1.4 the fundamental tensor and the cartan tensor
references for chapter 1
chapter 2 the chern connection
2.0 prologue
2.1 the vector bundle tm and related objects
2.2 coordinate bases versus special orthonormal bases
2.3 the nonlinear connection on the manifold tm
2.4 the chern connection on tm
2.5 index gymnastics
references for chapter 2
chapter 3 curvature and schur's lemma
3.1 conventions and the hh-, hv-, w-curvatures
3.2 first bianchi identities from torsion freeness
3.3 formulas for r and p in natural coordinates
3.4 first bianchi identities from "almost" g-compatibility
3.5 second bianchi identities
3.6 interchange formulas or ricci identities
3.7 lie brackets among the and the
3.8 derivatives of the geodesic spray coefficients gi
3.9 the flag curvature
3.10 schur's lemma
references for chapter 3
chapter 4 finsler surfaces and a generalized gauss-bonnet theorem
4.0 prologue
4.1 minkowski planes and a useful basis
4.2 the equivalence problem for minkowski planes
4.3 the berwald frame and our geometrical setup on sm
4.4 the chern connection and the invariants i, j, k
4.5 the riemannian arc length of the indicatrix
4.6 a gauss-bonnet theorem for landsberg surfaces
references for chapter 4
part two calculus of variations and comparison theorems
chapter 5 variations of arc length,
chapter 6 the gauss lemma and the hopf-rinow theorem
chapter 7 the index form and the bonnet-myers theorem
chapter 8 the cut and conjugate loci, and synge's theorem
chapter 9 the cartan-hadamard theorem and rauch's first theorem
part three special finsler spaces over the reals
chapter 10 berwald spaces and szab6's theorem for berwald surfaces
chapter 11 randers spaces and an elegant theorem
chapter 12 constant flag curvature spaces and akbar-zadeh's theorem
chapter 13 riemannian manifolds and two of hopf's theorems
chapter 14 minkowski spaces, the theorems of deicke and brickell bibliography
index
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黎曼-芬斯勒幾何導論 節選
《黎曼:芬斯勒幾何導論(英文版)》是由世界圖書出版公司出版的。
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