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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2020 • Question 5

Question

Math 6510 • Differentiable Manifolds Summer 2020 • Question 5

Suppose that \(M\) and \(N\) are smooth surfaces in \(\mathbb {R}^3\) that intersect at a point \(p\) and that do not have the same tangent plane at that point. Show that \(p\) is not an isolated point of \(M\cap N\).

Raw LaTeX

Suppose that \(M\) and \(N\) are smooth surfaces in \(\R^3\) that intersect at a
point \(p\) and that do not have the same tangent plane at that point. Show that
\(p\) is not an isolated point of \(M\cap N\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups