From Dual Connections to Almost Contact Structures

A dualistic structure on a smooth Riemaniann manifold $M$ is a triple $(M,g,\mathrm{\nabla })$ with $g$ a Riemaniann metric and $\mathrm{\nabla }$ an affine connection, generally assumed to be torsionless. From $g$ and $\mathrm{\nabla }$, the dual connection ${\mathrm{\nabla }}^{\ast }$ can be defined and the triple $(M,\mathrm{\nabla },{\mathrm{\nabla }}^{\ast })$ 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.