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Connections compatible with tensors. A characterization of left-invariant Levi--Civita connections in Lie groups
Paolo Piccione, Daniel V. Tausk
Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distributi…
Spectral Flow, Maslov Index and Bifurcation of semi-Riemannian Geodesics
Paolo Piccione, Alessandro Portaluri, Daniel V. Tausk
We give a functional analytical proof of the equality between the Maslov index of a semi-Riemannian geodesic and the spectral flow of the path of self-adjoint Fredholm operators ob…
An Index Theory for Paths that are Solutions of a Class of Strongly Indefinite Variational Problems
Paolo Piccione, Daniel V. Tausk
We prove a generalized version of the Morse index theorem for geodesics endowed with a non positive definite metric tensor (semi-Riemannian manifolds). We apply the result to obtai…
The Morse Index Theorem in semi-Riemannian Geometry
Paolo Piccione, Daniel V. Tausk
We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two…
On the Distribution of Conjugate Points along semi-Riemannian Geodesics
Paolo Piccione, Daniel V. Tausk
Helfer in [Pacific J. Math. 164/2 (1994), p. 321--350] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we…
Variational aspects of the geodesic problem in sub-Riemannian geometry
Paolo Piccione, Daniel V. Tausk
We study the local geometry of the space of horizontal curves with endpoints freely varying in two given submanifolds and of a manifold endow…