From Dual Connections to Almost Contact Structures

Abstract

A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,∇) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection ∇* can be defined. In this work, we give conditions on the basis of this notion for a manifold to admit an almost contact structure and some related structures: almost contact metric, contact, contact metric, cosymplectic, and co-Kähler in the three-dimensional case.

Keywords

• dual connections
• autodual connections
• torsionless dual connections
• autodual torsionless connection (Levi-Civita connection)
• gauge equation of dual connections
• almost cosymplectic structure