arXiv subjects

Raúl Martínez-Bohórquez

Publications and source records attributed to Raúl Martínez-Bohórquez.

3 recordsLinked to original sources

arXiv2024

Dimensional curvature identities in Fedosov geometry

The curvature tensor of a symplectic connection, as well as its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less than or equal to a fixed n. In this paper, we prove certain results regarding these curvature identities. Our main result describes, for any fixed dimension and any even number p of indices, the first space (provided we have filtered the identities by a homogeneity condition) of p-covariant curvature identities. To this end, we use recent results on the theory of natural operations on Fedosov manifolds. These results allow us to apply the invariant theory of the symplectic group, with a method that is analogous to that used in Riemannian or Kahler geometry.

math.DG↗

arXiv2023

On the existence of the electromagnetic energy tensor in second order Lovelock gravities

In this work we prove that there are no electromagnetic energy tensors in second order Lovelock gravities that verify properties equivalent to those of the Maxwell electromagnetic energy tensor in General Relativity.

gr-qc↗

arXiv2023

On invariant operations of Fedosov structures

In this paper we study invariant local operations that can performed on a Fedosov manifold, with a particular emphasis on tensor-valued operations (also known as natural tensors). Our main result describes the spaces of homogeneous natural tensors as certain finite dimensional linear representations of the symplectic group.

math.DG↗