Manifolds: Current Research Areas
by Paul Bracken (ed.)
Publisher: InTech 2017
Number of pages: 158
Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas.
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by Anders Kock - University of Aarhus
This textbook can be used as a non-technical and geometric gateway to many aspects of differential geometry. The audience of the book is anybody with a reasonable mathematical maturity, who wants to learn some differential geometry.
by Taha Sochi - viXra
A collection of notes about differential geometry prepared as part of tutorials about topics and applications related to tensor calculus. They can be used as a reference for a first course on the subject or as part of a course on tensor calculus.
by Robert L. Bryant, et al. - MSRI
An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. This book gives a treatment of exterior differential systems. It includes both the theory and applications.
by Liviu I. Nicolaescu - University of Notre Dame
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.