From Dual Connections to Almost Contact Structures

Abstract: A dualistic structure on a smooth Riemaniann manifold $M$ is a triple $(M,g,\nabla)$ with $g$ a Riemaniann metric and $\nabla$ an affine connection, generally assumed to be torsionless. From $g$ and $\nabla$, the dual connection $\nabla^*$ can be defined and the triple $(M, \nabla,\nabla^*)$ 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 coK\"ahler in the three-dimensional case.