63 citations · 227 across the 25 of their papers we have counts for
4 papers · 1 filter
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…
A Morse Theory for Massive Particles and Photons in General Relativity
Fabio Giannoni, Antonio Masiello, Paolo Piccione
In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case…
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…