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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 2

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 2

For which values of \(a>0\) does the hyperboloid \[ x^2+y^2-z^2=1 \] intersect the sphere \(x^2+y^2+z^2=a\) transversally (in \(\mathbb {R}^3\))?

Raw LaTeX

For which values of \(a>0\) does the hyperboloid
\[
  x^2+y^2-z^2=1
\]
intersect the sphere \(x^2+y^2+z^2=a\) transversally (in \(\mathbb{R}^3\))?

Topic Tags

Transversality and Intersection Theory