MATH 657 - Representation of Continuous Groups

Institution:

University of Pennsylvania

Subject:

Description:

Staff. Possible topics: harmonic analysis on locally compact abelian groups; almost periodic functions; direct integral decomposition theory, Types I, II and III: induced representations, representation theory of semisimple groups. Differential Geometry. (M) Staff. Prerequisite(s): Math 600/601, Math 602/603. Riemannian metrics and connections, geodesics, completeness, Hopf-Rinow theorem, sectional curvature, Ricci curvature, scalar curvature, Jacobi fields, second fundamental form and Gauss equations, manifolds of constant curvature, first and second variation formulas, Bonnet-Myers theorem, comparison theorems, Morse index theorem, Hadamard theorem, Preissmann theorem, and further topics such as sphere theorems, critical points of distance functions, the soul theorem, Gromov-Hausdorff convergence. Differential Geometry. (M) Staff. Prerequisite(s): Math 660 or with the permission of the instructor. Continuation of Math 660.

Credits:

3.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.upenn.edu

Phone Number:

(215) 898-5000

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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