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Undergraduate and Graduate Programs 2019-2020

MATH 645 Riemannian Geometry I

Smooth Manifolds, Riemannian Metrics and Levi-Civita Connections. Covariant Differentiation of Vector Fields. Riemannian Manifolds. Curvature, Geodesics, Exponential Map, Normal Coordinates. Sectional, Ricci and Scalar Curvatures. Gradient, Divergence and Laplacian Operators. Riemannian Submanifolds, Induced Connection, Second Fundamental Form, Formulae of Gauss and Weingarten. Equations of Gauss, Codazzi and Ricci. Credit units: 3 ECTS Credit units: 5.

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