Quarter-Symmetric Metric Connection on a Cosymplectic Manifold

Abstract

We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define η-Einstein cosymplectic manifolds of the θ-th kind and prove that they coincide with the η-Einstein cosymplectic manifold.

Keywords

• almost-contact manifold
• cosymplectic manifold
• co-Kähler manifold
• quarter-symmetric connection
• <i>η</i>-Einstein manifold