Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection

Abstract

We study lightlike submanifolds of a semi-Riemannian product manifold. We introduce a class of lightlike submanifolds called screen semi-invariant lightlike submanifold. We consider lightlike submanifolds with respect to a quarter symmetric non-metric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection

“…If the linear connection ∇ is not a metric connection, then ∇ is called a quarter symmetric non-metric connection. A significant number of properties on lightlike submanifolds of an indefinite Kaehler manifold with quarter symmetric non-metric connection have been developed by [5], [6], [14], [16].…”

Altın semi-Riemann manifoldların semi-invaryant lightlike altmanifoldları

“…Later, Duggal and Şahin introduced a book on lightlike geometry [10]. Many authors have studied on lightlike submanifolds in various spaces, for example [2,3,4,5,8,9,16].…”

Curvature Tensors of Screen Semi-invariant Half-Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter-Symmetric Non-metric Connection

“…Various researchers [28], [14], [1], [16] have developed the geometry of submanifolds for semi-Riemannian manifolds equipped with quarter symmetric non-metric connection. In this context, the screen semi-invariant lightlike submanifolds for product semi-Riemannian manifold were introduced and studied extensively by [15].…”