Riemannian Submanifolds: A Survey
by Bang-Yen Chen
Publisher: arXiv 2013
Number of pages: 272
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.
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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 Richard L. Bishop - arXiv
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds.
by John Douglas Moore - University of California
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.
by Curtis McMullen - Harvard University
This course will concern the interaction between: hyperbolic geometry in dimensions 2 and 3, the dynamics of iterated rational maps, and the theory of Riemann surfaces and their deformations. Intended for advanced graduate students.