by Ilkka Holopainen, Tuomas Sahlsten
Number of pages: 102
Based on the lecture notes on differential geometry. From the table of contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.
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by M. Berger - Tata Institute of Fundamental Research
The main topic of these notes is geodesics. Our aim is to give a fairly complete treatment of the foundations of Riemannian geometry and to give global results for Riemannian manifolds which are subject to geometric conditions of various types.
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.
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.
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.