In this article, we derive Chen’s inequalities involving ?-invariant ?M, Riemannian invariant ?(m1,?,mk), Ricci curvature, ?k(2?k?m), the scalar curvature and squared of mean for submanifolds generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application obtain inequality, first derived Chen inequality bi-slant submanifold Sasakian-space-forms.

We propose fundamental inequalities for contact pseudo-slant submanifolds of (ϵ)-para Sasakian space form employing generalized normalized δ-Casorati curvature. characterize which equality cases hold and illustrate the main result with some applications. Further, we have considered a certain type submanifold Ricci soliton after computing its scalar curvature, developed an inequality to find cor...

In this paper, we introduce the new notion of quasi bi-slant submanifolds almost Hermitian manifolds. Necessary and sufficient conditions for integrability distributions which are involved in definition such a Kaehler manifold obtained. We also investigate necessary these manifolds to be totally geodesic study geometry foliations determined by above distributions. Finally, obtain submanifold lo...

The purpose of this paper is to provide the complete classifications second fundamental form inequality for a warped product pointwise semi-slant submanifold in Kaehler manifold which was obtained by Şahin [Th. 5.2, Warped manifold, Port. Math. 2013] terms intrinsic and extrinsic invariants. In paper, we give some conditions that are not addressed or considered cited mentioned above. Finally, n...

In this paper, we prove that every pointwise semi-slant warped product submanifold M = NT xf N? in a nearly Kenmotsu manifold ?M satisfies the following inequality: ||h||2 ? 2n2 (1 + 10/9 cot2?)(|| ??(lnf)||2-1), where n2 dimN?, ??(ln f) is gradient of ln f and ||h|| length second fundamental form M. The equality special cases inequality are investigated.

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen studied Lagrangian submanifolds in complex space forms which are ideal. He proved that such submanifolds are minimal. He also classified ideal Lagrangian submani...

In this study, the authors focus on quasi-hemi-slant submanifolds (qhs-submanifolds) of (α,β)-type almost contact manifolds, also known as trans-Sasakian manifolds. Essentially, we give sufficient and necessary conditions for integrability distributions using concept We consider geometry foliations dictated by distribution requirements manifolds with factors to be totally geodesic. Lastly, an i...

In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant helices}. Also, we present some characterizations theorems for $k$-slant helices and derived, in general form, the intrinsic equations for such curves. Thereafter, fr...

this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.