Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1996 • Question 18

Question

Math 6510 • Differentiable Manifolds Fall 1996 • Question 18

Prove that torus can not be immersed in \(\mathbb {R}^3\) in such a way that the Gauss curvature of the induced metric is everywhere non-negative.

Raw LaTeX

Prove that torus can not be immersed in \(\mathbb{R}^3\) in such a way
that the Gauss curvature of the induced metric is everywhere non-negative.

Topic Tags

Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups