Riemannian Geometry
by Richard L. Bishop
Publisher: arXiv 2013
Number of pages: 67
Description:
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds. Affine connections, geodesics, torsion and curvature, the exponential map, and the Riemannian connection follow quickly.
Download or read it online for free here:
Download link
(580KB, PDF)
Similar books
![Book cover: A Panoramic View of Riemannian Geometry](images/5637.jpg)
by Marcel Berger - Springer
In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. The book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading.
(12144 views)
![Book cover: Riemannian Geometry: Definitions, Pictures, and Results](images/10923.jpg)
by Adam Marsh - arXiv
A pedagogical but concise overview of Riemannian geometry is provided in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions and relevant theorems.
(6905 views)
![Book cover: Semi-Riemann Geometry and General Relativity](images/blank.gif)
by Shlomo Sternberg
Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.
(18515 views)
![Book cover: Holonomy Groups in Riemannian Geometry](images/8248.jpg)
by Andrew Clarke, Bianca Santoro - arXiv
The holonomy group is one of the fundamental analytical objects that one can define on a Riemannian manfold. These notes provide a first introduction to the main general ideas on the study of the holonomy groups of a Riemannian manifold.
(8375 views)