MATH823
Riemannian Geometry

Course Description

This course covers Riemannian metrics; connections and covariant differentiation; Riemannian curvature tensor, sectional curvature, Ricci curvature and scalar curvature; Riemannian submanifolds; parallelism, geodesics, Hopf-Rinow theorem; first and second variation of arc length, Jacobi fields; Bochner techniques, Bonnet- Myers


Prerequisite

Differentiable manifolds, Differential geometry of curves and surfaces, or their equivalent


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