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1.

図書
図書
1. An introduction to Riemann-Finsler geometry (: hbk)
D. Bao, S.-S. Chern, Z. Shen
出版情報: New York : Springer-Verlag, c2000  xx, 431 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 200
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目次情報: 続きを見る
Preface
Acknowledgments
Finsler Manifolds and Their Curvature / Part 1：
Finsler Manifolds and the Fundamentals of Minkowski Norms / Chapter 1：
Physical Motivations / 1.0：
Finsler Structures: Definitions and Conventions / 1.1：
Two Basic Properties of Minkowski Norms / 1.2：
Euler's Theorem / 1.2 A.：
A Fundamental Inequality / 1.2 B.：
Interpretations of the Fundamental Inequality / 1.2 C.：
Explicit Examples of Finsler Manifolds / 1.3：
Minkowski and Locally Minkowski Spaces / 1.3 A.：
Riemannian Manifolds / 1.3 B.：
Randers Spaces / 1.3 C.：
Berwald Spaces / 1.3 D.：
Finsler Spaces of Constant Flag Curvature / 1.3 E.：
The Fundamental Tensor and the Cartan Tensor / 1.4：
References for Chapter 1
The Chern Connection / Chapter 2：
Prologue / 2.0：
The Vector Bundle [pi]*TM and Related Objects / 2.1：
Coordinate Bases Versus Special Orthonormal Bases / 2.2：
The Nonlinear Connection on the Manifold TM \ 0 / 2.3：
The Chern Connection on [pi]*TM / 2.4：
Index Gymnastics / 2.5：
The Slash (...)[subscript / 2.5 A.：
Covariant Derivatives of the Fundamental Tensor g / 2.5 B.：
Covariant Derivatives of the Distinguished l / 2.5 C.：
References for Chapter 2
Curvature and Schur's Lemma / Chapter 3：
Conventions and the hh-, hv-, vv-curvatures / 3.1：
First Bianchi Identities from Torsion Freeness / 3.2：
Formulas for R and P in Natural Coordinates / 3.3：
First Bianchi Identities from "Almost" g-compatibility / 3.4：
Consequences from the dx[superscript k] [logical and] dx[superscript l] Terms / 3.4 A.：
Consequences from the dx[superscript k] [logical and] 1/F[delta]y[superscript 1] Terms / 3.4 B.：
Consequences from the 1/F[delta]y[superscript k] [logical and] 1/F[delta]y[superscript 1] Terms / 3.4 C.：
Second Bianchi Identities / 3.5：
Interchange Formulas or Ricci Identities / 3.6：
Lie Brackets among the [delta]/[delta]x and the F[characters not reproducible] / 3.7：
Derivatives of the Geodesic Spray Coefficients G[superscript i] / 3.8：
The Flag Curvature / 3.9：
Its Definition and Its Predecessor / 3.9 A.：
An Interesting Family of Examples of Numata Type / 3.9 B.：
Schur's Lemma / 3.10：
References for Chapter 3
Finsler Surfaces and a Generalized Gauss-Bonnet Theorem / Chapter 4：
Minkowski Planes and a Useful Basis / 4.0：
Rund's Differential Equation and Its Consequence / 4.1 A.：
A Criterion for Checking Strong Convexity / 4.1 B.：
The Equivalence Problem for Minkowski Planes / 4.2：
The Berwald Frame and Our Geometrical Setup on SM / 4.3：
The Chern Connection and the Invariants I, J, K / 4.4：
The Riemannian Arc Length of the Indicatrix / 4.5：
A Gauss-Bonnet Theorem for Landsberg Surfaces / 4.6：
References for Chapter 4
Calculus of Variations and Comparison Theorems / Part 2：
Variations of Arc Length, Jacobi Fields, the Effect of Curvature / Chapter 5：
The First Variation of Arc Length / 5.1：
The Second Variation of Arc Length / 5.2：
Geodesics and the Exponential Map / 5.3：
Jacobi Fields / 5.4：
How the Flag Curvature's Sign Influences Geodesic Rays / 5.5：
References for Chapter 5
The Gauss Lemma and the Hopf-Rinow Theorem / Chapter 6：
The Gauss Lemma / 6.1：
The Gauss Lemma Proper / 6.1 A.：
An Alternative Form of the Lemma / 6.1 B.：
Is the Exponential Map Ever a Local Isometry? / 6.1 C.：
Finsler Manifolds and Metric Spaces / 6.2：
A Useful Technical Lemma / 6.2 A.：
Forward Metric Balls and Metric Spheres / 6.2 B.：
The Manifold Topology Versus the Metric Topology / 6.2 C.：
Forward Cauchy Sequences, Forward Completeness / 6.2 D.：
Short Geodesics Are Minimizing / 6.3：
The Smoothness of Distance Functions / 6.4：
On Minkowski Spaces / 6.4 A.：
On Finsler Manifolds / 6.4 B.：
Long Minimizing Geodesics / 6.5：
The Hopf-Rinow Theorem / 6.6：
References for Chapter 6
The Index Form and the Bonnet-Myers Theorem / Chapter 7：
Conjugate Points / 7.1：
The Index Form / 7.2：
What Happens in the Absence of Conjugate Points? / 7.3：
Geodesics Are Shortest Among "Nearby" Curves / 7.3 A.：
A Basic Index Lemma / 7.3 B.：
What Happens If Conjugate Points Are Present? / 7.4：
The Cut Point Versus the First Conjugate Point / 7.5：
Ricci Curvatures / 7.6：
The Ricci Scalar Ric and the Ricci Tensor Ric[subscript ij] / 7.6 A.：
The Interplay between Ric and Ric[subscript ij] / 7.6 B.：
The Bonnet-Myers Theorem / 7.7：
References for Chapter 7
The Cut and Conjugate Loci, and Synge's Theorem / Chapter 8：
Definitions / 8.1：
The Cut Point and the First Conjugate Point / 8.2：
Some Consequences of the Inverse Function Theorem / 8.3：
The Manner in Which c[subscript y] and i[subscript y] Depend on y / 8.4：
Generic Properties of the Cut Locus Cut[subscript x] / 8.5：
Additional Properties of Cut[subscript x] When M Is Compact / 8.6：
Shortest Geodesics within Homotopy Classes / 8.7：
Synge's Theorem / 8.8：
References for Chapter 8
The Cartan-Hadamard Theorem and Rauch's First Theorem / Chapter 9：
Estimating the Growth of Jacobi Fields / 9.1：
When Do Local Diffeomorphisms Become Covering Maps? / 9.2：
Some Consequences of the Covering Homotopy Theorem / 9.3：
The Cartan-Hadamard Theorem / 9.4：
Prelude to Rauch's Theorem / 9.5：
Transplanting Vector Fields / 9.5 A.：
A Second Basic Property of the Index Form / 9.5 B.：
Flag Curvature Versus Conjugate Points / 9.5 C.：
Rauch's First Comparison Theorem / 9.6：
Jacobi Fields on Space Forms / 9.7：
Applications of Rauch's Theorem / 9.8：
References for Chapter 9
Special Finsler Spaces over the Reals / Part 3：
Berwald Spaces and Szabo's Theorem for Berwald Surfaces / Chapter 10：
Various Characterizations of Berwald Spaces / 10.0：
Examples of Berwald Spaces / 10.3：
A Fact about Flat Linear Connections / 10.4：
Characterizing Locally Minkowski Spaces by Curvature / 10.5：
Szabo's Rigidity Theorem for Berwald Surfaces / 10.6：
The Theorem and Its Proof / 10.6 A.：
Distinguishing between y-local and y-global / 10.6 B.：
References for Chapter 10
Randers Spaces and an Elegant Theorem / Chapter 11：
The Importance of Randers Spaces / 11.0：
Randers Spaces, Positivity, and Strong Convexity / 11.1：
A Matrix Result and Its Consequences / 11.2：
The Geodesic Spray Coefficients of a Randers Metric / 11.3：
The Nonlinear Connection for Randers Spaces / 11.4：
A Useful and Elegant Theorem / 11.5：
The Construction of y-global Berwald Spaces / 11.6：
The Algorithm / 11.6 A.：
An Explicit Example in Three Dimensions / 11.6 B.：
References for Chapter 11
Constant Flag Curvature Spaces and Akbar-Zadeh's Theorem / Chapter 12：
Characterizations of Constant Flag Curvature / 12.0：
Useful Interpretations of E and E / 12.2：
Growth Rates of Solutions of E + [lambda]E = 0 / 12.3：
Akbar-Zadeh's Rigidity Theorem / 12.4：
Formulas for Machine Computations of K / 12.5：
The Geodesic Spray Coefficients / 12.5 A.：
The Predecessor of the Flag Curvature / 12.5 B.：
Maple Codes for the Gaussian Curvature / 12.5 C.：
A Poincare Disc That Is Only Forward Complete / 12.6：
The Example and Its Yasuda-Shimada Pedigree / 12.6 A.：
The Finsler Function and Its Gaussian Curvature / 12.6 B.：
Geodesics; Forward and Backward Metric Discs / 12.6 C.：
Consistency with Akbar-Zadeh's Rigidity Theorem / 12.6 D.：
Non-Riemannian Projectively Flat S[superscript 2] with K = 1 / 12.7：
Bryant's 2-parameter Family of Finsler Structures / 12.7 A.：
A Specific Finsler Metric from That Family / 12.7 B.：
References for Chapter 12
Riemannian Manifolds and Two of Hopf's Theorems / Chapter 13：
The Levi-Civita (Christoffel) Connection / 13.1：
Curvature / 13.2：
Symmetries, Bianchi Identities, the Ricci Identity / 13.2 A.：
Sectional Curvature / 13.2 B.：
Ricci Curvature and Einstein Metrics / 13.2 C.：
Warped Products and Riemannian Space Forms / 13.3：
One Special Class of Warped Products / 13.3 A.：
Spheres and Spaces of Constant Curvature / 13.3 B.：
Standard Models of Riemannian Space Forms / 13.3 C.：
Hopf's Classification of Riemannian Space Forms / 13.4：
The Divergence Lemma and Hopf's Theorem / 13.5：
The Weitzenbock Formula and the Bochner Technique / 13.6：
References for Chapter 13
Minkowski Spaces, the Theorems of Deicke and Brickell / Chapter 14：
Generalities and Examples / 14.1：
The Riemannian Curvature of Each Minkowski Space / 14.2：
The Riemannian Laplacian in Spherical Coordinates / 14.3：
Deicke's Theorem / 14.4：
The Extrinsic Curvature of the Level Spheres of F / 14.5：
The Gauss Equations / 14.6：
The Blaschke-Santalo Inequality / 14.7：
The Legendre Transformation / 14.8：
A Mixed-Volume Inequality, and Brickell's Theorem / 14.9：
References for Chapter 14
Bibliography
Index
Preface
Acknowledgments
Finsler Manifolds and Their Curvature / Part 1：
2.

図書
図書
2. Partial differential equations : proceedings of a symposium held in Tianjin, June 23-July 5, 1986 (: gw ; : us)
S.S. Chern [ed.]
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  vi, 294 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1306 . Nankai Institute of Mathematics, Tianjin, P.R. China ; v. 3
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3.

図書
図書
3. Differentiable manifolds : forms, currents, harmonic forms (: gw ; : us ; : pbk)
Georges de Rham ; translated from the French by F.R. Smith ; introduction to the English edition by S.S. Chern
出版情報: Berlin ; New York : Springer-Verlag, 1984  x, 166 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 266
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4.

図書
図書
4. Selected papers ([v. 1] : us - v. 4 : gw)
Shiing-shen Chern
出版情報: New York ; Tokyo : Springer-Verlag, c1978-c1989  4 v. ; 25 cm
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5.

図書
図書
5. Seminar on nonlinear partial differential equations
edited by S.S. Chern
出版情報: New York : Springer-Verlag, c1984  373 p. ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 2
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6.

図書
図書
6. Lectures on differential geometry (: pbk)
S.S. Chern, W.H. Chen, K.S. Lam
出版情報: Singapore : World Scientific, c1999  x, 356 p.
シリーズ名: Series on university mathematics ; vol. 1
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7.

図書
図書
7. Differential geometry : Cartan's generalization of Klein's Erlangen program (: hard)
R.W. Sharpe ; foreword by S.S. Chern
出版情報: New York : Springer, c1997  xix, 421 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 166
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目次情報: 続きを見る
In the Ashes of the Ether: Differential Topology
Looking for the Forest in the Leaves: Folations
The Fundamental Theorem of Calculus
Shapes Fantastic: Klein Geometries
Shapes High Fantastical: Cartan Geometries
Riemannian Geometry
Mwbius Geometry
Projective Geometry
In the Ashes of the Ether: Differential Topology
Looking for the Forest in the Leaves: Folations
The Fundamental Theorem of Calculus
8.

図書
図書
8. A mathematician and his mathematical work : selected papers of S.S. Chern
edited by S.Y. Cheng, P. Li, G. Tian
出版情報: Singapore ; New Jersey : World Scientific, c1996  xiv, 707 p. ; 26 cm
シリーズ名: World Scientific series in 20th century mathematics ; vol. 4
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9.

図書
図書
9. Proceedings of the 1982 Changchun Symposium on Differential Geometry and Differential Equations = 1982年"双微"長春討論会文集
chief editors, S.S. Chern, Wang Rou-huai, Chi Min-you
出版情報: Beijing, China : Science Press, 1986  xi, 765 p. ; 25 cm
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10.

図書
図書
10. Proceedings of the 1983 Beijing Symposium on Differential Geometry and Differential Equations = 1983年"双微"北京討論会文集
cheif editor, Liao Shantao, with advice from S.S. Chern
出版情報: Beijing, China : Science Press, 1986  vii, 604 p. ; 25 cm
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