MATH 6620

MATH 6620

Course information provided by the Courses of Study 2018-2019.

Topics include linear connections, Riemannian metrics and parallel translation; covariant differentiation and curvature tensors; the exponential map, the Gauss Lemma and completeness of the metric; isometries and space forms, Jacobi fields and the theorem of Cartan-Hadamard; the first and second variation formulas; the index form of Morse and the theorem of Bonnet-Myers; the Rauch, Hessian, and Laplacian comparison theorems; the Morse index theorem; the conjugate and cut loci; and submanifolds and the Second Fundamental form.

When Offered Spring.

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Syllabi: none
  •   Regular Academic Session. 

  • 4 Credits Stdnt Opt

  • 16153 MATH 6620   LEC 001