Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2013 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2013 • Question 3

Let \(S\subset \mathbb {R}^3\) be a (nonempty) smooth surface. Prove that there exists a plane \(ax+by+cz=d\) in \(\mathbb {R}^3\) whose intersection with \(S\) is a collection of circles and lines.

Raw LaTeX

Let \(S\subset\R^3\) be a (nonempty) smooth surface. Prove that there exists a
plane \(ax+by+cz=d\) in \(\R^3\) whose intersection with \(S\) is a collection of
circles and lines.

Topic Tags

Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups Transversality and Intersection Theory