8 citations · 13 across the 10 of their papers we have counts for
12 papers · 1 filter
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…
Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds
Miguel Angel Javaloyes, Paolo Piccione
We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the c…
Partial Signatures and the Yoshida-Nicolaescu Theorem
José Carlos Corrêa Eidam, Paolo Piccione
In this article, we give a simple and direct proof of the Yoshida-Nicolaescu Theorem in a more general context by using the theory of partial signatures. We do not impose the usual…
On the Maslov index of symplectic paths that are not transversal to the Maslov cycle. Semi-Riemannian index theorems in the degenerate case
R. Giambo, P. Piccione, A. Portaluri
We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the cas…
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…