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Semi-slant submanifolds of a nearly Kaehler manifold

The aim in the present paper is to study some basic geometric properties of semi-slant submanifolds of a nearly Kaehler manifold. | Turk J Math 31 (2007) , 341 – 353. ¨ ITAK ˙ c TUB Semi-Slant Submanifolds of a Nearly Kaehler Manifold Viqar Azam Khan and Meraj Ali Khan Abstract The aim in the present paper is to study some basic geometric properties of semi-slant submanifolds of a nearly Kaehler manifold. Key words and phrases: Slant, Semi-slant, totally umbilical, totally geodesic. 1. Introduction Slant submanifolds of a Kaehler manifold have been studied extensively in [2], [3], [4] [5] etc., whereas slant submanifolds of a nearly Kaehler manifold are yet to be explored to that extent. A nearly Kaehler structure on a manifold provides an interesting study with differential geometric point of view (c.f., [7], [8] etc. ), consequently, the study of submanifolds of a nearly Kaehler manifold vis-a-vis that of a Kaehler manifold assumes significance in general. The study of differential geometry of semi-slant submanifolds, as a generalized version of CR-submanifolds of a Kaehlerian manifold was initiated by N. Papaghiuc [10]. Our aim, in the present note is to extend the study and explore some basic geometric aspects of semi-slant submanifolds of a nearly Kaehler manifold some of which have already been studied in the setting of a Kaehler manifold. The paper is organized in the following way. In section 2, we recall some necessary details of almost Hermitian , nearly Kaehler manifolds and their submanifolds to provide some pre-requisites for the succeeding sections. In section 3, we have obtained some results regarding the integrability and the 2000 AMS Mathematics Subject Classification: 53C40; 53B25. 341 KHAN, KHAN parallelism of the distributions on a semi-slant submanifold of an almost Hermitian manifold. In fact, this section intends to make a foundation for studying differential geometry of the semi-slant submanifolds of a nearly Kaehler manifold. Section 4 deals with the integrability of the distributions on the semi-slant submanifolds of a nearly Kaehler manifold and some important .