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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1997 • Question 16

Question

Math 6510 • Differentiable Manifolds Fall 1997 • Question 16

Define what a Riemannian manifold is. Define the natural distance function which one obtains from the (infinitesimal) Riemannian metric, and prove that this distance function gives a metric space structure to each Riemannian manifold.

Raw LaTeX

Define what a Riemannian manifold is. Define the natural distance
function which one obtains from the (infinitesimal) Riemannian metric, and prove that
this distance function gives a metric space structure to each Riemannian manifold.

Topic Tags

Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds