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.
In this article, we obtain the necessary and sufficient conditions that the semiinvariant submanifold to be a locally warped product submanifold of invariant and anti-invariant submanifolds of a cosymplectic manifold in terms of canonical structures T and F. The inequality and equality cases are also discussed for the squared norm of the second fundamental form in terms of the warping function. 2000 AMS Mathematics Subject Classification: 53C25; 53C40; 53C42; 53D15.
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.
Recently, we have shown that there do not exist the warped product semi-slant submanifolds of cosymplectic manifolds [10].As nearly cosymplectic structure generalizes cosymplectic ones same as nearly Kaehler generalizes Kaehler structure in almost Hermitian setting. It is interesting that the warped product semi-slant submanifolds exist in nearly cosymplectic case while in case of cosymplectic do not exist. In the beginning, we prove some preparatory results and finally we obtain an inequality such as h 2 ≥ 4q csc 2 θ{1 + 1 9 cos 2 θ} ∇ ln f 2 in terms of intrinsic and extrinsic invariants. The equality case is also considered.2010 AMS Mathematics Subject Classification: 53C40, 53C42, 53C15.
We study semi-slant warped product submanifolds of a Kenmotsu manifold. We obtain a characterization for warped product submanifolds in terms of warping function and shape operator and finally proved an inequality for squared norm of second fundamental form.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.