From Dual Connections to Almost Contact Structures
Résumé
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.
Mots clés
dual connections
auto-dual connections
torsionless dual connections
auto-dual torsionless connection(Levi-Civita connection)
gauge equation of dual connections
almost cosymplectic structure
almost symplectic structure
symplectic structure
cosymplectic structure
almost contact structure
almost contact metric structure
coKhaler structure
