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Some properties of the spectral flow in semiriemannian geometry

✍ Scribed by Vieri Benci; Fabio Giannoni; Antonio Masiello

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
779 KB
Volume
27
Category
Article
ISSN
0393-0440

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✦ Synopsis

Let f(z) = 1; g(z)[i , i] ds be the action integral on a semiriemannian manifold (M, g) defined on the space of the curves z : [0, l] + M joining two given points zo and ~1. The critical points of f are the geodesics joining zo and ZI. Let s E [0, 11. We study the behavior, in dependence of s, of the eigenvalues of the Hessian form of f evaluated at z, restricted to the interval [0, s]. A formula for the derivative of the eigenvalues is given and some applications are shown.

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