On a semi-symmetric non-metric connection

Abstract

H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection on a Riemannian manifold in (1932). Agashe and Chafle [1] defined and studied semi-symmetric non-metric connection on a Riemannian manifold. In the present paper, we define a new type of semi-symmetric non-metric connexion in an almost contact metric manifold and studied its properties. In the end, we have studied some properties of the covariant almost analytic vector field equipped with semisymmetric non-metric connection.2000 Mathematics Subject Classification : 53B15.

On a semi-symmetric non-metric connection

“…for arbitrary vector fields X and Y , is said to be a semi-symmetric non-metric connection [1].The torsion tensorS of the connectionB and the metric tensor g are given byS…”

Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection

“…Since then, the properties of the quarter-symmetric metric (non-metric) connections on different structures have been studied by many geometers. For more details, we refer ( [3], [5], [9], [21], [23], [25], [27]) and the references there in.…”

A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection

“…Several authors such as Pravonovich [14], Agashe and Chafle [1], Liang [12] and Sengupta, De and Binh [16] introduced a semi-symmetric non-metric connection in different ways and this connection is studied by many authors [7,16,18], etc.... Recently, Chaubey and Ojha [4,5] defined a new type of semi-symmetric non-metric connection in an almost contact metric manifold. In 2011, These authors [6] studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.…”

“…Recently, Chaubey and Ojha [4,5] defined a new type of semi-symmetric non-metric connection in an almost contact metric manifold. In 2011, These authors [6] studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.…”