IJPAM: Volume 79, No. 3 (2012)

SECTIONAL CURVATURE OF A CR-SUBMANIFOLD OF
$(\kappa,\mu)$-CONTACT METRIC MANIFOLDS WITH
VANISHING $GC$-BOCHNER CURVATURE TENSOR

Reem Al-Ghefari
Department of Mathematics
Faculity of Science
King AbdulAziz University
P.O. Box 126300, Jeddah, 21352, KINGDOM OF SAUDI ARABIA


Abstract. CR-submanifold of a Kaehler manifold have been defined by Bejaneu [1] and studied by many authors. On the other hand CR-submanifold of a Sasakian manifold have been studied by Matsumoto [6] and others. Moreover, CR-submanifolds of Sasakian manifold with vanishing contact Bochner curvature tensor was studied by Shahid [7]. In [3], the author studied $%
(\kappa,\mu)$-contact metric manifold for which the characteristic vector field $\xi$ belongs to the $(\kappa,\mu)$ nullity distribution. The class of $(\kappa,\mu)$-contact metric manifold contains the class of Sasakian manifold which we obtain for $\kappa=1.$ The aim of this note is to study CR-submanifolds of $(\kappa,\mu)$-contact metric manifold with vanishing generalized contact (GC-) Bochner curvature tensor.

Received: May 15, 2012

AMS Subject Classification: 53C20, 53C45

Key Words and Phrases: CR-submanifold, $(\kappa,\mu)$-contact metric manifolds, $GC$-Bochner curvature tensor

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 3