Some results on cosymplectic manifolds

TL;DR

This paper generalizes stability theorems for cosymplectic structures and characterizes compact solvmanifolds with such structures as finite quotients of tori.

Contribution

It extends the Kodaira-Morrow stability theorem to cosymplectic structures and classifies compact solvmanifolds admitting these structures.

Findings

A compact solvmanifold admits a cosymplectic structure iff it is a finite quotient of a torus.

Generalization of the Kodaira-Morrow stability theorem for cosymplectic structures.

Investigation of cosymplectic geometry on Lie groups and their quotients.

Abstract

We obtain a generalization of the Kodaira-Morrow stability theorem for cosymplectic structures. We investigate cosymplectic geometry on Lie groups and on their compact quotients by uniform discrete subgroups. In this way we show that a compact solvmanifold admits a cosymplectic structure if and only if it is a finite quotient of a torus.