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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2020 • Question 2

Question

Math 6510 • Differentiable Manifolds Spring 2020 • Question 2

Let \(X,Y\subset \mathbb {R}^3\) be smooth 1-dimensional submanifolds. Show that there is a \(v\in \mathbb {R}^3\) such that \(X\) is disjoint from \(Y+v=\{y+v:y\in Y\}\).

Raw LaTeX

Let \(X,Y\subset\R^3\) be smooth 1-dimensional submanifolds. Show that there
is a \(v\in\R^3\) such that \(X\) is disjoint from
\(Y+v=\{y+v:y\in Y\}\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds