A Sampler of Riemann-Finsler Geometry (Mathematical Sciences Research Institute Publications, Series Number 50)

Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. This book presents an expository account of seven important topics in Riemann-Finsler geometry, ones which have recently undergone significant development but have not had a detailed pedagogical treatment elsewhere. Each article will open the door to an active area of research, and is suitable for a special topics course in graduate-level differential geometry. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry, and parametrized jet bundles, and include a variety of instructive examples. This Book Presents An Expository Account Of Seven Important Topics In Riemann-finsler Geometry, Which Have Recently Undergone Significant Development But Have Not Had A Detailed Pedagogical Treatment Elsewhere. Each Article Will Open The Door To An Active Area Of Research And Is Suitable For A Special Topics Course In Graduate-level Differential Geometry.--jacket. Volumes On Normed And Finsler Spaces / J.c. Alvarez Paiva And A.c. Thompson -- Anisotropic And Crystalline Mean Curvature Flow / Giovanni Bellettini -- Finsler Geometry On Complex Vector Bundles / Tadashi Aikou -- Finsler Geometry Of Holomorphic Jet Bundles / Karen Chandler And Pit-mann Wong -- Ricci And Flag Curvatures In Finsler Geometry / David Bao And Colleen Robles -- Nonreversible Finsler Metrics Of Positive Flag Curvature / Hans-bert Rademacher -- Landsberg Curvature, S-curvature And Riemann Curvature / Zhongmin Shen. Edited By David Bao ... [et Al.]. Includes Bibliographical References And Index. Volumes on normed and Finsler spaces / J.C. Álvarez Paiva and A.C. Thompson Anisotropic and crystalline mean curvature flow / Giovanni Bellettini Finsler geometry on complex vector bundles / Tadashi Aikou Finsler geometry of holomorphic jet bundles / Karen Chandler and Pit-Mann Wong Ricci and flag curvatures in Finsler geometry / David Bao and Colleen Robles Nonreversible Finsler metrics of positive flag curvature / Hans-Bert Rademacher Landsberg curvature, S-curvature and Riemann curvature / Zhongmin Shen Finsler geometry generalizes Riemannian geometry in exactly the same way that Banach spaces generalize Hilbert spaces. This book presents expository accounts of six important topics in Finsler geometry at a level suitable for a special topics graduate course in differential geometry. The contributors consider issues related to volume, geodesics, curvature and mathematical biology, and include a variety of instructive examples. This book presents expository accounts of six important topics in Finsler geometry suitable for a special-topics graduate course in differential geometry. They treat issues related to volume, geodesics, curvature and mathematical biology, and provide a good variety of instructive examples. fm.pdf......Page 1 00cont.pdf......Page 7 00pref.pdf......Page 8 01syn.pdf......Page 10 02AT.pdf......Page 12 03Be.pdf......Page 60 04Ai.pdf......Page 94 05CW.pdf......Page 117 06BR.pdf......Page 208 07Ra.pdf......Page 271 08Sh.pdf......Page 314 09ind.pdf......Page 367 The study of volumes and areas on normed and Finsler spaces is a relatively new field that comprises and unifies large domains of convexity, geometric tomography, and integral geometry. These expository accounts treat issues related to volume, geodesics, curvature and mathematical biology, with instructive examples.