Busemann regular G-spaces
著者
書誌事項
Busemann regular G-spaces
（Reviews in mathematics and mathematical physics, v. 10,
Harwood Academic Pub., c1998
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内容説明・目次
内容説明
G-Spaces are finitely compact metric spaces in which the condition of extensibility of the shortest curve locally holds. Sufficiently regular Finsler spaces, in particular, Riemannian spaces, are G-Spaces.
The book is intended for students, post-graduate students and specialized researchers of mathematics.
目次
Introduction
Chapter 1. G-spaces
1.1. Metric Space 1.2. Curves in a metric space 1.3. Shortest curves 1.4. G-space 1.5. Minkowski space
Chapter 2. Finsler spaces which are G-spaces
2.1 Finsler space 2.2. Smoothness of shortest curves 2.3. Equations of geodesic curves 2.4. Uniqueness of shortest curves 2.5. Example of a Finsler space which is not a G-space.
Chapter 3. G-spaces which are Finsler spaces
3.1. The slope of shortest curves 3.2. Finite dimensionality of a space 3.3. Topological structure of a space 3.4. Proof of Theorem 1
Chapter 4. G-spaces which are Riemannian spaces
4.1. Axiom A' 4.2. Proof of Theorem 1
Chapter 5. Plane G-spaces
5.1. Examples of plane G-spaces 5.2 Averaging of plane metrics 5.3. Approximation of the metric of a plane G-space with Finsler plane metrics of the class C 5.4. General representation of the metrics of plane G-spaces
Chapter 6. Riemannian plane G-spaces
6.1. The Beltrami theorem 6.2. Proof of Theorem 1 in the two-dimensional case 6.3. Proof of Theorem 1 in the general case
References
Index
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