Linear Connections on Normal Almost Contact Manifolds with Norden Metric

TL;DR

This paper constructs and analyzes specific linear connections on normal almost contact manifolds with Norden metric, focusing on their curvature properties and introducing an analogue to the Yano connection.

Contribution

It introduces a new linear connection analogous to the Yano connection on normal almost contact manifolds with Norden metric, and studies its curvature properties.

Findings

Curvature properties are characterized for the new connection.

The connection is constructed on two basic classes of manifolds.

An analogue to the symmetric Yano connection is established.

Abstract

Families of linear connections are constructed on almost contact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connection are studied on two basic classes of normal almost contact manifolds with Norden metric.