Mathematics 369: Topics in Differential Geometry
(Spring 2005)
Instructor
Hubert Bray
Description
The motivation for this course will be to discuss the mathematical and
geometric aspects of General Relativity. As is well known,
General Relativity is Einstein's theory of gravity which replaced
Newtonian physics as the most experimentally verified theory of gravity
currently known. In addition, General Relativity motivates a
great deal of very interesting question in Differential Geometry.
In this course we will study many of these problems which will involve
minimal surfaces (which are related to black holes), manifolds with
nonnegative scalar curvature, and various geometric flows including
inverse mean curvature flow. We will also discuss related
mathematical topics such as the Yamabe problem, Ricci flow, and the
classification of 3-manifolds.
Prerequisites
Mathematics 267 (Differential Geometry). Specifically I will
assume that the students are
familiar with standard topics in Riemannian geometry: manifolds,
metrics,
connections, curvature, and differential forms.
Text(s)
Semi-Riemannian Geometry
(with Applications to Relativity) by Barrett O'Neill.
(This book is an excellent book to add to your collection.
However, we will place the book on reserve at the library as well.)
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Last modified October 29, 2004