Let f(z) = integral(0)(1) g(Z)[(z) over dot, (z) over dot] ds be the action integral on a semiriemannian manifold (M, g) defined on the space of the curves z : [0, 1] --> M joining two given points z(0) and z(1). The critical points of f are the geodesics joining z(0) and z(1). Let s is an element of [0, 1]. 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.
Some properties of the spectral flow in semiriemannian geometry / Benci, V.; Giannoni, F.; Masiello, A.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 27:3-4(1998), pp. 267-280. [10.1016/S0393-0440(97)00083-1]
Some properties of the spectral flow in semiriemannian geometry
Masiello, A.
1998-01-01
Abstract
Let f(z) = integral(0)(1) g(Z)[(z) over dot, (z) over dot] ds be the action integral on a semiriemannian manifold (M, g) defined on the space of the curves z : [0, 1] --> M joining two given points z(0) and z(1). The critical points of f are the geodesics joining z(0) and z(1). Let s is an element of [0, 1]. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
