Almost bi-slant submanifolds of an almost contact metric manifold
- PDF / 434,577 Bytes
- 23 Pages / 439.37 x 666.142 pts Page_size
- 3 Downloads / 200 Views
Journal of Geometry
Almost bi-slant submanifolds of an almost contact metric manifold Selcen Y¨ uksel Perkta¸s, Adara M. Blaga , and Erol Kılı¸c Abstract. In this paper we introduce and study the almost bi-slant submanifolds of an almost contact metric manifold. We give some characterization theorems for almost bi-slant submanifolds. Moreover, we obtain integrability conditions of the distributions which are involved in the definition of almost bi-slant submanifolds. We also get some results for totally geodesic and totally umbilical almost bi-slant submanifolds of cosymplectic manifolds and Sasakian manifolds. Mathematics Subject Classification. 53C15, 53C25, 53C40. Keywords. Almost contact metric manifold, cosymplectic manifold, Sasakian manifold, slant submanifold, bi-slant submanifold, almost bi-slant submanifold.
1. Introduction The geometry of slant submanifolds has shown an increasing development in the last decades. The theory of slant immersions in complex geometry was introduced by Chen [9,10] as a generalization of both holomorphic and totally real submanifolds. Later, slant submanifolds have been studied by many geometers in various manifolds (see [16,17]). In 1996, Lotta [14] introduced the notion of slant submanifold of an almost contact metric manifold. In [7,8] the authors studied and characterized slant submanifolds of K-contact and Sasakian manifolds. Recently, the study of semi-slant submanifolds was initiated by Papaghiuc [15] as a generalization of CR-submanifolds. In Cabrerizo et al. [6] defined and studied a contact version of semi-slant submanifolds. They also introduced A part of this paper was presented by the first author as Almost bi-slant submanifolds of an almost contact manifold in VIII-th Geometry Symposium, Akdeniz University, 29 April–2 May, 2010, Antalya, Turkey. 0123456789().: V,-vol
2
Page 2 of 23
S. Y. Perkta¸s et al.
J. Geom.
a more general class of submanifolds, namely bi-slant submanifolds (see also [2,11,13]). On the other hand, in Bejancu [3] initiated the study of CR-submanifolds of an almost Hermitian manifold by generalizing invariant and anti-invariant submanifolds. Bejancu and Papaghiuc [4] extended this concept to submanifolds of almost contact metric manifolds and they called such submanifolds as semiinvariant submanifolds. Later, the study of almost semi-invariant submanifolds of framed metric manifolds, as a generalization of both CR-submanifolds and semi-invariant submanifolds, was introduced by Tripathi and Singh [21] (see also [18–20]). In the present paper, we introduce almost bi-slant submanifolds of an almost contact metric manifold which can be considered as a generalization of bislant and almost semi-invariant submanifolds. Section 2 is devoted to some basic definitions and formulae for an almost contact metric manifold and its submanifolds. In Sect. 3, we introduce the notion of almost bi-slant submanifolds of an almost contact metric manifold. In Sect. 4, we investigate integrability conditions of the distributions which are involved in the definiti
Data Loading...
