Almost Cosymplectic $p$-Spheres and Almost Cosymplectic Metric Bi-Structures on Three-Manifolds

Abstract:

      The purpose of this paper is to study almost cosymplectic $p$-spheres and almost cosymplectic metric bi-structures. Firstly, we show some properties of almost cosymplectic $p$-spheres. Then we introduce the notion of almost cosymplectic metric bi-structures and give some results on three dimensional manifolds admitting almost cosymplectic metric bi-structures. Moreover, we investigate three dimensional manifolds with almost cosymplectic metric bi-structures when the $(1, 1)$-type tensor fields $h_1$ and $h_2$ are being of codazzi type and cyclic parallel.