43 citations · 131 across the 31 of their papers we have counts for
12 papers · 1 filter
An existence theorem for G-structure preserving affine immersions
Paolo Piccione, Daniel V. Tausk
We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and…
The single-leaf Frobenius Theorem with Applications
Paolo Piccione, Daniel V. Tausk
Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a…
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…