A Sampler of 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 A Sampler of Riemann-Finsler Geometry write by David Dai-Wai Bao. This book was released on 2004-11. A Sampler of Riemann-Finsler Geometry available in PDF, EPUB and Kindle. These expository accounts treat issues related to volume, geodesics, curvature and mathematical biology, with instructive examples.
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 David Dai-Wai Bao. This book was released on 2000. An Introduction to Riemann-Finsler Geometry available in PDF, EPUB and Kindle.
Riemann-Finsler Geometry
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 Riemann-Finsler Geometry write by Shiing-Shen Chern. This book was released on 2005. Riemann-Finsler Geometry available in PDF, EPUB and Kindle. Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann-Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar curvature or isotropic S-curvature, etc. Instructive examples are given in abundance, for further description of some important geometric concepts. The text includes the most recent results, although many of the problems discussed are classical. Graduate students and researchers in differential geometry.
Finsler Geometry
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 Finsler Geometry write by Xinyue Cheng. This book was released on 2013-01-29. Finsler Geometry available in PDF, EPUB and Kindle. "Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields. Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.
Comparison Finsler Geometry
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.
