ABSTRACT. In the present note we have obtained some basic results pertaining to the geometry of slant and semi-slant submanifolds of a Kenmotsu manifold.

ABSTRACT. Warped product manifolds are known to have applications in Physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star (cf. [HONG, S. T.: Warped products and black holes, Nuovo Cimento Soc. Ital. Fis. B 120 (2005), 1227-1234]). The studies on warped product manifolds with extrinsic geometric point of view are intensified after B. Y. Chen's work on CR-warped product submanifolds of Kaehler manifolds. Later on, similar studies are carried out in the setting of Sasakian manifolds by Hasegawa and Mihai. As Kenmotsu manifolds are themselves warped product spaces, it is interesting to investigate warped product submanifolds of Kenmotsu manifolds. In the present note a larger class of warped product submanifolds than the class of contact CR-warped product submanifolds is considered. More precisely the existence of warped product submanifolds of a Kenmotsu manifold with one of the factors an invariant submanifold is ensured, an example of such submanifolds is provided and a characterization for a contact CR-submanifold to be a contact CR-warped product submanifold is established.

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Abstract. J. L. Cabrerizo et al.[5] studied slant submanifolds of Sasakian and Kcontact manifolds. Semi-slant submanifolds were introduced as a generalized version of CR-submanifold. Cabrerizo et al. [4] obtained interesting results for the semi-slant submanifold of Sasakian manifolds. The purpose of the present paper is to study slant and semi-slant submanifolds of a T-manifold. IntroductionThe study of differential geometry of slant submanifolds of a Kaehler manifold was initiated by B. Y. Chen [9]. Later, A. Lotta [10] extended the study of the slant immersions in contact manifolds. N. Papaghiuc [11] introduced the notion of semi-slant submanifold of almost Hermitian manifolds, which is in fact a generalization of CR-submanifold. Cabrerizo et al. [4] extended the idea of semi-slant submanifold to the setting of Sasakian manifold. C. Calin [6] studied CR-submanifold of a T-manifold. To extend this study it is important to investigate semi-slant submanifolds of a T-manifold. PreliminariesLet M be a (2n + s)-dimensional differentiate manifold of class C°° endowed with a (f>-structure of rank 2n. According to Blair [3], the is said to be a complemented frame if there exist structure vector fields £ 2 ,..., and its dual 1-forms 771,772, • • •, % such thatwhere 5a denotes the Kronecker delta and a, ¡3 = 1,..., s.1991 Mathematics Subject Classification: 53C40; 53B25.