International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 11, Pages 681-686
doi:10.1155/S0161171202011390
On a class of even-dimensional manifolds structured by an affine connection
I. Mihai1
, A. Oiagă1
and R. Rosca3
1Faculty of Mathematics, Str. Academiei 14, Bucharest 70109, Romania
359 Avenue Emile Zola, Paris 75015, France
Abstract
We deal with a 2m-dimensional Riemannian manifold (M,g) structured by an affine connection and a vector field 𝒯, defining a 𝒯-parallel connection. It is proved that 𝒯 is both a torse forming vector field and an exterior concurrent vector field. Properties of the curvature 2-forms are established. It is shown that M is endowed with a conformal symplectic structure Ω and 𝒯 defines a relative conformal transformation of Ω.