Is calculus on manifolds a good book?

3.0 out of 5 starsVery well known classic, but… With its instantly recognizable cover, Calculus on Manifolds (1965) is a classic and for cultural reasons, every serious math/theoretical physics grad student should have read this deceptively slim volume by his/her first year of grad school.

What is differential geometry manifold?

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas.

What is the best book to learn about manifolds?

If you prefer a transition from differential curves and surfaces focusing on riemannian geometry you have Kühnel- “Differential Geometry: Curves, Surfaces, Manifolds”. However, I would argue that one of the best introductions to manifolds is the old soviet book published by MIR, Mishchenko/Fomenko- “A Course of Differential Geometry and Topology”.

What is the best book for differential geometry of manifolds?

A little bit more advanced and dealing extensively with differential geometry of manifolds is the book by Jeffrey Lee- “Manifolds and Differential Geometry”(do not confuse it with the other books by John M. Lee which are also nice but too many and too long to cover the same material for my tastes).

What are some good books similar to TU’s manifolds?

If you look for an alternative to Tu’s I believe the best one is John M. Lee – “Introduction to Smooth Manifolds”; it is a well-written book with a slow pace covering every elementary construction on manifolds and its table of contents is very similar to Tu’s.

Is the book Topological manifolds worth getting into?

It depends on what you are interested in. In my opinion “topological manifolds” is just a book about topology, most titles when considering manifolds mean “smooth” ones since differential geometry works mainly in that category. One usually has already taken a course in topology when getting into manifolds.