From Dual Connections to Almost Contact Structures
Emmanuel Gnandi, Stéphane Puechmorel · arXiv (Cornell University) · 2022
A dualistic structure on a smooth Riemaniann manifold $M$ is a triple $(M,g, abla)$ with $g$ a Riemaniann metric and $ abla$ an affine connection, generally assumed to be torsionless. From $g$ and $ abla$, the dual connection $ abla^*$ can be defined and the triple $(M, abla, abla^*)$ is called a statistical manifold, a basic object in information geometry. In this work, we give conditions based on this notion for a manifold to admit an almost contact structure and some related structures: almost contact metric,contact, contact metric, cosymplectic, and coKähler in the three-dimensional case.