DIFFERENTIAL GEOMETRY

MATH 765

Course Description

Covers the metric properties of Riemannian manifolds. The following topics will be covered: Vector bundles and connections, Riemannian metrics, submanifolds and second fundamental form, first variation of arc length, geodesics, Hopf-Rinow theorem, second variation of arc length, Jacobi fields and index lemmas, Bonnet-Meyer theorem, Rauch comparison theorem, spaces of constant curvature, Hodge-de Rham theory. Familiarity with the topics in a differential manifolds course (e.g.MATH 761) is strongly recommended.

Prerequisties

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

Satisfies

This course does not satisfy any prerequisites.

Credits

Not Reported

Offered

Not Reported

Grade Point Average

3.48% from Historical

Completion Rate

100%

1.46% from Historical

A Rate

100%

7.22% from Historical

Class Size

-10.1% from Historical

Instructors (2025 Fall)

Sorted by ratings from Rate My Professors

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