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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1996 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 1996 • Question 1

Let \(M\) be the Moebius band which has Riemannian metric with totally-geodesic boundary and curvature \(K(p)\le 0\) in all points \(p\in M\). Show that the curvature of this metric is identically zero.

Raw LaTeX

Let \(M\) be the Moebius band which has Riemannian metric with
totally-geodesic boundary and curvature \(K(p)\le 0\) in all points \(p\in M\). Show that
the curvature of this metric is identically zero.

Topic Tags

Smooth Manifolds and Embedded Submanifolds