P. Piccione

Publications164
h-index21
Citations1,578
Highly Influential Citations74
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Partial Representations and Partial Group Algebras
Abstract The partial group algebra of a group G over a field K , denoted by K par ( G ), is the algebra whose representations correspond to the partial representations of G over K -vector spaces. In…
An intrinsic approach to the Geodesical Connectedness of Stationary Lorentzian Manifolds
We prove a variational principle for geodesies on a Lorentzian manifold M. admitting a timelike Killing vector field. Using this principle and standard techniques of global nonlinear analysis we…
On bifurcation of solutions of the Yamabe problem in product manifolds
An existence theorem for G-structure preserving affine immersions
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 semi-Riemannian…
A note on the uniqueness of solutions for the Yamabe problem
We prove that in conformal classes of metrics near the class of an Einstein metric (other than the standard round metric on a sphere) the Yamabe problem has a unique solution up to scaling. This is a…
The Morse index theorem in semi-Riemannian geometry
Teichmüller theory and collapse of flat manifolds
We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat…
An analytical theory for Riemannian cubic polynomials
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical…
On Fermat's principle for causal curves in time oriented Finsler spacetimes
In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the second variation of the time arrival functional…
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