If you're interested in learning differential geometry, I recommend checking out the following books:
For students and researchers, these lectures are often used as a "second-year" graduate text. While it assumes a basic knowledge of manifolds and tensors, it is indispensable for anyone moving into . schoen yau lectures on differential geometry pdf
The text bridges the gap between classical differential geometry and modern analysis, focusing heavily on how are used to solve geometric and topological problems . Key topics covered include: If you're interested in learning differential geometry, I
Studying this PDF is a rite of passage. After mastering these notes, a student is prepared to: Key topics covered include: Studying this PDF is
The notes teach you how to use PDE estimates (Sobolev inequalities, Harnack inequalities) not just as analysis tools, but as geometric construction tools. You learn how to "solve for a geometric object" rather than just calculating properties of given objects.
The availability of these notes (often circulated as PDFs within math departments before formal publication) has been pivotal for the field of .
The text is celebrated for its deep dive into several critical areas of differential geometry: