This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a uni

"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham co

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential

Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis

From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.