Riv.Mat.Univ.Parma (4) 17 (1991)


Biconformal cosymplectic manifolds

Pages: 41-58
Received: 8 July 1990
Mathematics Subject Classification: 53C15

Abstract Let M be Riemannian (2m + 1)-dimensional C -manifold endowed with a structure 2-form Ω, a structure 1-form η and a structure vector field ξ dual to η. As a generalization of conformal cosymplectic manifolds, M (Ω, η ξ g) is defined in the present paper as a "biconformal cosymplectic manifolds" if both structure forms Ω and η are "cohomologically closed". With such a structure denoted by B.C. Sp(sm + 1, R) is associated a closed 1-form w and its dual vector W. Different properties of the dω-cohomology and the Lie algebra on M involving η u, Ω, W and ξ are discussed. If Mh is the hypersurface normal to ξ, the following salient properties are established: (a) If M is a conformal cosymplectic manifold, the Mh is a symplectic manifold. (b) If M is a biconformal cosymplectic manifold, then Mh is a conformal symplectic manifold. As an application, we get the necessary and sufficient condition for a (2m + 1)-dimensional quasi-Sasakian manifold M (Φ, Ω, η, ξ, g) to be endowed with a B.C.-structure. Some striking properties of invariant and anti-invariant submanifolds of a B.C.-quasi-Sasakian manifold are discussed.