Plenty of Morse functions by perturbing with sums of squares

Details Plenty of Morse functions by perturbing with sums of squares Plenty of Morse functions by perturbing with sums of squares

2011-11-16

arxiv.org/abs/1111.3851v1

Mathematics

Differential Geometry

Scientific paper

Given a smooth function f on R^n and a submanifold M, we prove that the set
of diagonal quadratic forms q such that the restriction of f+q to M is Morse is
a dense set (in the n-dimensional space of diagonal quadratic forms). The
standard transversality argument seems not to work and we need a more refined
approach.

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