Comparison Finsler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Comparison Finsler Geometry write by Shin-ichi Ohta. This book was released on 2021-10-09. Comparison Finsler Geometry available in PDF, EPUB and Kindle. This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.
Introduction To Modern Finsler Geometry
Introduction To Modern Finsler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction To Modern Finsler Geometry write by Yi-bing Shen. This book was released on 2016-02-25. Introduction To Modern Finsler Geometry available in PDF, EPUB and Kindle. 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.
Lectures on Finsler Geometry
Lectures on Finsler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Finsler Geometry write by Zhongmin Shen. This book was released on 2001. Lectures on Finsler Geometry available in PDF, EPUB and Kindle. 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. Contents: Finsler Spaces; Finsler m Spaces; Co-Area Formula; Isoperimetric Inequalities; Geodesics and Connection; Riemann Curvature; Non-Riemannian Curvatures; Structure Equations; Finsler Spaces of Constant Curvature; Second Variation Formula; Geodesics and Exponential Map; Conjugate Radius and Injectivity Radius; Basic Comparison Theorems; Geometry of Hypersurfaces; Geometry of Metric Spheres; Volume Comparison Theorems; Morse Theory of Loop Spaces; Vanishing Theorems for Homotopy Groups; Spaces of Finsler Spaces. Readership: Graduate students and researchers in geometry and physics.
An Introduction to Riemann-Finsler Geometry
An Introduction to Riemann-Finsler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Riemann-Finsler Geometry write by D. Bao. This book was released on 2012-12-06. An Introduction to Riemann-Finsler Geometry available in PDF, EPUB and Kindle. This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.
Introduction to Modern Finsler Geometry
Introduction to Modern Finsler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Modern Finsler Geometry write by Yibing Shen. This book was released on 2016. Introduction to Modern Finsler Geometry available in PDF, EPUB and Kindle. 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.
