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Introduction to modern Finsler geometry / Yi-Bing Shen and Zhongmin Shen.

By: Contributor(s): Material type: TextTextPublication details: Singapore : World Scientific, ©2016.Description: xii, 393 pages ; 24 cmISBN:
  • 9789814704908
Subject(s): DDC classification:
  • 516.375 23 Sh546
Contents:
1. Differentiable manifolds -- 2. Finsler metrics -- 3. Connections and curvatures -- 4. S-curvature -- 5. Riemann curvature -- 6. Projective changes -- 7. Comparison theorems -- 8. Fundamental groups of Finsler manifolds -- 9. Minimal immersions and harmonic maps -- 10. Einstein metrics -- 11. Miscellaneous topics.
Summary: This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
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Includes bibliographical references and index.

1. Differentiable manifolds --
2. Finsler metrics --
3. Connections and curvatures --
4. S-curvature --
5. Riemann curvature --
6. Projective changes --
7. Comparison theorems --
8. Fundamental groups of Finsler manifolds --
9. Minimal immersions and harmonic maps --
10. Einstein metrics --
11. Miscellaneous topics.

This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.

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