Lectures on Geodesics in Riemannian Geometry
by M. Berger
Publisher: Tata Institute of Fundamental Research 1965
Number of pages: 317
Description:
The main topic of these notes is geodesics. Our aim is 1) to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it and 2) to give global results for Riemannian manifolds which are subject to geometric conditions of various types; these conditions involve essentially geodesics.
Download or read it online for free here:
Download link
(1.5MB, PDF)
Similar books
Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computationby M. Arnaudon, F. Barbaresco, L. Yang - arXiv
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. The existence and uniqueness results of local medians are given. We propose a subgradient algorithm and prove its convergence.
(10091 views)
Holonomy Groups in Riemannian Geometryby 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.
(8377 views)
Riemannian Geometry: Definitions, Pictures, and Resultsby 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.
(6908 views)
A Panoramic View of Riemannian Geometryby 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)