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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2024 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 2024 • Question 1

For which \(a > 0\) do the surfaces

\[ M=\{x^2+y^2-z^2=1\}\subset \mathbb {R}^3 \quad \text {and}\quad N=\{x^2+y^2+z^2=a\}\subset \mathbb {R}^3 \]

have nonempty transverse intersection?

Raw LaTeX

For which \(a > 0\) do the surfaces

\[
M=\{x^2+y^2-z^2=1\}\subset\mathbb{R}^3
\quad\text{and}\quad
N=\{x^2+y^2+z^2=a\}\subset\mathbb{R}^3
\]

have nonempty transverse intersection?

Topic Tags

Smooth Manifolds and Embedded Submanifolds Transversality and Intersection Theory