8 citations · 13 across the 10 of their papers we have counts for
21 papers
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…
On the Homotopy Type of the Fredholm Lagrangian Grassmannian
José Carlos Corrêa Eidam, Paolo Piccione
In this article, we show that the Fredholm Lagrangian Grassmannian is homotopy equivalent with the space of compact perturbations of a fixed lagrangian. As a corollary, we obtain t…
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…
Orthogonal Geodesic Chords, Brake Orbits and Homoclinic Orbits in Riemannian Manifolds
Roberto Giambó, Fabio Giannoni, Paolo Piccione
The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis--Jacobi variational principle, to the st…
Complementary Lagrangians in Infinite Dimensional Symplectic Hilbert Spaces
Paolo Piccione, Daniel V. Tausk
Using the Spectral Theorem for unbounded self-adjoint operators we prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementa…