مقدمه‌ای بر منیفولدهای تفاضلی و هندسه ریمانی، ویرایش بازنگری‌شده (جلد ۱۲۰) (ریاضیات خالص و کاربردی، جلد ۱۲۰)

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 Introduction to Manifolds; Functions of Several Variables and Mappings; Differentiable Manifolds and Submanifolds; Vector Fields on a Manifold; Tensors and Tensor Fields on Manifolds; Integration on Manifolds; Differentiation on Riemannian Manifolds; Curvature; Index The Second Edition Of This Text Has Sold Over 6,000 Copies Since Publication In 1986 And This Revision Will Make It Even More Useful. This Is The Only Book Available That Is Approachable By Beginners In This Subject. It Has Become An Essential Introduction To The Subject For Mathematics Students, Engineers, Physicists, And Economists Who Need To Learn How To Apply These Vital Methods. It Is Also The Only Book That Thoroughly Reviews Certain Areas Of Advanced Calculus That Are Necessary To Understand The Subject. I. Introduction To Manifolds -- Ii. Functions Of Several Variables And Mappings -- Iii. Differentiable Manifolds And Submanifolds -- Iv. Vector Fields On A Manifold -- V. Tensors And Tensor Fields On Manifolds -- Vi. Integration On Manifolds -- Vii. Differentiation On Riemannian Manifolds -- Viii. Curvature. William M. Boothby. Previous Ed.: 1986. Includes Bibliographical References (p. 403-409) And Index. The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. In this chapter, we establish some preliminary notations and give an intuitive, geometric discussion of a number of examples of manifolds-the primary objects of study throughout the book.