CR-submanifolds of (LCS)n-manifolds with respect to quarter symmetric non-metric connection

Abstract

The present paper deals with the study of CR-submanifolds of (LCS) n-manifolds with respect to quarter symmetric non-metric connection. We investigate integrability of the distributions and the geometry of foliations. The totally umbilical CR-submanifolds of said ambient manifolds are also studied. An example is presented to illustrate the results.

Quarter-symmetric non-metric connection

“…This paper aims to research the quarter-symmetric non-metric connection on a generalized Riemannian manifold. Recently, many papers studied quarter-symmetric non-metric connection on various manifolds (for example, see [7,12,17,18,23,24]).…”

Contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection

“…M. Ahmad studied CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with quarter symmetric metric connection [1] and T. Pal et al discussed CR-submanifolds of (LCS) n -manifolds with respect to quarter symmetric non-metric connection [16] in detail.…”

“…Motivated from all the research papers mentioned above and specially from the work done by T. Pal et al [16], in this paper we have studied contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection. We have investigated totally geodesic leaves and integrability of the distributions and also have studied the totally umbilical contact CR-submanifolds of trans-Sasakian manifolds.…”

Solitons of η-Ricci–Bourguignon Type on Submanifolds in (LCS)m Manifolds

“…where (X, Y, Z) are the standard coordinates in R 3 (shown in [44]). The linearly independent vector fields at each point of S are denoted by E i for i = {1, 2, 3} such that…”

“…By applying Koszul's formula, the RC of S (see [44]) can be obtained easily; hence, the components Ricci of the Ricci tensor of S are as follows:…”