Compact cosymplectic manifolds with transversally positive definite Ricci tensor

Abstract

In this paper we study compact cosymplectic manifolds with transversally positive definite Ricci tensor, that is, compact cosymplectic manifolds such that its Ricci tensor is positive definite on vector fields orthogonal to the Reeb vector field of the cosymplectic structure. We prove that the fundamental group of a cosymplectic manifold M with transversally positive definite Ricci tensor is isomorphic to ZZ and, in particular, if M is of positive constant ϕ-sectional curvature we show that there exists a certain cosymplectic structure on the product of a complex projective space of positive constant holomorphic sectional curvature with the circle S1 such that M is almost contact isometric to such a product.

Keywords

• cosymplectic manifolds
• ricci tensor
• transversally positive definite
• fundamental group
• ϕ-sectional curvature
• complex projective space