Lectures on Differential Geometry
by John Douglas Moore
Publisher: University of California 2009
Number of pages: 263
This course will describe the foundations of Riemannian geometry, including geodesics and curvature, as well as connections in vector bundles, and then go on to discuss the relationships between curvature and topology. Topology will presented in two dual contrasting forms, de Rham cohomology and Morse homology.
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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 David R. Wilkins - Trinity College, Dublin
From the table of contents: Smooth Manifolds; Tangent Spaces; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; Jacobi Fields.
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.
by Bang-Yen Chen - arXiv
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. In this book, the author provides a broad review of Riemannian submanifolds in differential geometry.