Some Geometric Properties of Spacetime - Lecture 2

Explore key geometric properties of spacetime in this lecture by Richard Schoen from UC Irvine, USA, delivered at the ICTP School on Geometry and Gravity. Delve into topics such as the Top and AH Graph Theorem, dihedral angles, and local theorems. Examine the positive mass theorem and its implications for nonnegative scalar curvature. Investigate the second fundamental form and the Gauss-Bonnet theorem. Gain insights into the mathematical foundations of spacetime geometry and its relevance to gravity theory through this comprehensive presentation.

Introduction
Last time
Top and AH Graph Theorem
Dihedral angles
Local theorems
Positive mass theorem
Nonnegative scalar curvature
Second fundamental form
Gauss Benet theorem