8 citations · 22 across the 21 of their papers we have counts for
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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…
An Index Theorem for Non Periodic Solutions of Hamiltonian Systems
Paolo Piccione, Daniel Victor Tausk
We consider a {\em Hamiltonian setup} $\sextuple$, where is a symplectic manifold, is a distribution of Lagrangian subspaces in , $\mathc…
A Generalized Index Theorem for Morse-Sturm Systems and Applications to semi-Riemannian Geometry
F. Giannoni, A. Masiello, P. Piccione +1
We prove an extension of the Index Theorem for Morse-Sturm systems of the form , where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus…
The Fermat Principle in General Relativity and Applications
Fabio Giannoni, Antonio Masiello, Paolo Piccione
In this paper we use a general version of Fermat's principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining…
Morse Theory for the Travel Time Brachistochrones in Stationary Spacetimes
Fabio Giannoni, Paolo Piccione, Daniel V. Tausk
The travel time brachistochrone curves in a general relativistic framework are timelike curves, satisfying a suitable conservation law with respect to a an observer field, that are…
Stability of the Focal and Geometric Index in semi-Riemannian Geometry via the Maslov Index
Francesco Mercuri, Paolo Piccione, Daniel V. Tausk
We investigate the problem of the stability of the number of conjugate or focal points (counted with multiplicity) along a semi-Riemannian geodesic . For a Riemannian or a non s…