Codazzi and statistical connections on almost product manifolds

Abstract

Considering an almost product manifold, we get the necessary and sufficient conditions for Codazzi connections on it. Also, we show that a Codazzi adapted connection on an almost product manifold, gives two type of Codazzi connections on it’s distributions, and moreover we study the conditions of holding the converse of this. Finally, we study the Codazzi ( and statistical ) structures for Schouten-Van Kampen and Vr ̆anceanu connections as two important special cases of adapted connections, and then we present some important examples of them.