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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2018 • Question 1

Question

Math 6510 • Differentiable Manifolds Summer 2018 • Question 1

Let \(M\) be the smooth submanifold of \(\mathbb {R}^3\) consisting of points that satisfy \(x^2+y^2-z^2=1\). Let \(N\) be the smooth submanifold of \(\mathbb {R}^3\) consisting of points that satisfy \(x+y+z=0\). Prove that \(M\cap N\) is a smooth manifold.

Raw LaTeX

Let \(M\) be the smooth submanifold of \(\R^3\) consisting of points that
satisfy \(x^2+y^2-z^2=1\). Let \(N\) be the smooth submanifold of \(\R^3\) consisting
of points that satisfy \(x+y+z=0\). Prove that \(M\cap N\) is a smooth manifold.

Topic Tags

Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds