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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2005 • Question 1

Question

Math 6510 • Differentiable Manifolds Winter 2005 • Question 1

Let \[ X=\{(x,y)\in \mathbb {R}^3\times \mathbb {R}^3 \mid x\cdot x=y\cdot y=1,\ x\cdot y=0\}. \] Show that \(X\) is a submanifold of \(\mathbb {R}^3\times \mathbb {R}^3\).

Raw LaTeX

Let
\[
  X=\{(x,y)\in\mathbb{R}^3\times\mathbb{R}^3
  \mid x\cdot x=y\cdot y=1,\ x\cdot y=0\}.
\]
Show that \(X\) is a submanifold of \(\mathbb{R}^3\times\mathbb{R}^3\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds