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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 11, Pages 681-686

On a class of even-dimensional manifolds structured by an affine connection

1Faculty of Mathematics, Str. Academiei 14, Bucharest 70109, Romania
259 Avenue Emile Zola, Paris 75015, France

Received 16 January 2001; Revised 29 June 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.