Fundamentals of differential geometry graduate texts. Differential geometry graduate texts in mathematics. Jorgensonlang analytic number theory and connections with spectral analysis, heat kernel, differential geometry, lie groups, and symmetric. In dierential geometry, one putsanadditionalstructureonthedierentiablemanifoldavector. A highquality ocr scan of the original latin dg paper 37 pages. This book, fundamentals of differential geometry, by the exceptionally prolific serge lang, is useful as background for such practical purposes, but i would characterize its main focus as the high art or high culture of differential geometry.
Fundamentals of differential geometry serge lang auth. It is highculture mathematics for the sake of furthering the high art of mathematics. The size of the book influenced where to stop, and there would be enough material for a second volume this is not a threat. In differential topology, one studies for instance homotopy classes of maps and the. The size of the book influenced where to stop, and there would be. Home fundamentals of differential geometry graduate texts in mathematics. Springer have made a bunch of books available for free. Serge lang fundamentals of differential geometry world. Fundamentals of differential geometry springerlink. Geometric functional analysis and its applications, richard b. Operations on vector fields and differential forms.
Serge lang, fundamentals of differential geometry 1999. For example, lang presents almost all of differential geometry with general banach spaces for the. Introduction to differentiable manifolds serge lang. Introduction to differentiable manifolds, second edition. Fundamentals of differential geometry serge lang springer. Formally,onemaysaythatonestudies propertiesinvariantunderthegroupofdierentiableautomorphismswhich. The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry.