From Dual Connections to Almost Contact Structures

Emmanuel Gnandi and Stéphane Puechmorel ()
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Emmanuel Gnandi: Ecole Nationale de l’Aviation Civile, Université de Toulouse, 31055 Toulouse, France
Stéphane Puechmorel: Ecole Nationale de l’Aviation Civile, Université de Toulouse, 31055 Toulouse, France

Mathematics, 2022, vol. 10, issue 20, 1-20

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; almost symplectic structure; symplectic structure; cosymplectic structure; almost contact structure; almost contact metric structure; co-Khaler structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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