An Introduction to Differentiable Manifolds and Riemannian Geometry

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie

Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and s

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great ex

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical