A Comprehensive Introduction To Differential Geometry Volume 2

A comprehensive introduction to differential geometry

Proceedings of the International Conference on Geometry, Analysis and Applications

Geometrical concepts play a significant role in the analysis of physical systems. Apart from the intrinsic interest, the knowledge of differentiable manifolds has become useful ? even mandatory ? in an ever-increasing number of areas of mathematics and its applications. Many results/concepts in analysis find their most natural (generalized) setting in manifold theory. An interrelation of geometry and analysis can be found in this volume.The book presents original research, besides a few survey articles by eminent experts from all over the world on current trends of research in differential and algebraic geometry, classical and modern analysis including the theory of distributions (linear and nonlinear), partial differential equations and wavelets.

Lectures on Differential Geometry

Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern?Gauss?Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincar‚ and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds. The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.