On contact sub-pseudo-Riemannian isometries

TL;DR

This paper investigates the symmetries of contact sub-pseudo-Riemannian manifolds, establishing an upper bound on their isometry groups and identifying cases where this maximum is achieved, notably on the Heisenberg group.

Contribution

It provides a universal upper bound on the dimension of isometry groups in contact sub-pseudo-Riemannian geometry and characterizes structures attaining this bound.

Findings

Maximum isometry group dimension is achieved on the Heisenberg group.

Universal upper bound on isometry group dimension for contact sub-pseudo-Riemannian manifolds.

Left invariant structures on the Heisenberg group realize the maximal symmetry.

Abstract

We study isometries in the contact sub-pseudo-Riemannian geometry. In particular we give an upper bound on the dimension of the isometry group of a general sub-pseudo-Riemannian manifold and prove that the maximal dimension is attained for the left invariant structures on the Heisenberg group.