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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2007 • Question 8

Question

Math 6510 • Differentiable Manifolds Fall 2007 • Question 8

Suppose \(X\) is a smooth submanifold of \(\mathbb {R}^3\) and a nonempty closed surface. Prove that there is a plane \(P\subset \mathbb {R}^3\) such that \(X\cap P\) is a nonempty collection of circles.

Raw LaTeX

Suppose \(X\) is a smooth submanifold of \(\R^3\) and a nonempty closed surface.
Prove that there is a plane \(P\subset\R^3\) such that \(X\cap P\) is a nonempty
collection of circles.

Topic Tags

Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups