tailieunhanh - Point-wise slant submanifolds in almost contact geometry

In this paper, we introduce point-wise slant submanifolds of almost contact and almost contact 3-structure manifolds. We characterize them, give some examples, and obtain necessary and sufficient conditions for a point-wise slant submanifold of a 3-Sasakian manifold to be a slant submanifold. | Turk J Math (2016) 40: 657 – 664 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Point-wise slant submanifolds in almost contact geometry Mohammad Bagher KAZEMI BALGESHIR∗ Department of Mathematics, University of Zanjan, Zanjan, Iran Received: • Accepted/Published Online: • Final Version: Abstract: In this paper, we introduce point-wise slant submanifolds of almost contact and almost contact 3-structure manifolds. We characterize them, give some examples, and obtain necessary and sufficient conditions for a point-wise slant submanifold of a 3-Sasakian manifold to be a slant submanifold. Moreover, we show that there exist no proper Sasakian point-wise 3-slant submanifolds. Key words: Sasakian manifold, point-wise slant submanifold 1. Introduction Chen [4] generalized the notion of totally real and holomorphic submanifolds in complex geometry by introducing slant submanifolds. In [11], Lotta studied slant submanifolds of contact manifolds that were the generalization of invariant and anti-invariant submanifolds. Since then, many authors have obtained important and interesting results about slant submanifolds of complex [13, 14, 16, 17] and almost contact [1, 3, 8, 12] manifolds. On the other hand, Etayo [6] has extended this type of submanifold by defining quasi-slant submanifolds. In such submanifolds, at any given point, the slant angle is independent of the choice of any nonzero vector field of submanifold. Later, Chen and Garay [5] studied and characterized these submanifolds under the name pointwise slant submanifolds. Recently, Sahin showed [15] the existence of warped product point-wise semislant submanifolds of Kaehler manifolds, contrary to the semislant case. He and Lee [10] also investigated point-wise slant submersion from almost Hermitian manifolds. The importance of slant submanifolds in almost contact geometry motivated us to define .