Lectures on the geometry of manifolds/ Liviu I Nicolaescu

Includes bibliography and index

Manifolds -- Natural constructions on manifolds -- Calculus on manifolds -- Riemannian geometry -- Elements of the calculus of variations -- The fundamental group and covering spaces -- Cohomology -- Characteristic classes -- Classical integral geometry -- Elliptic equations on manifolds -- Spectral geometry -- Dirac operators

This book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.