Introduction Inthe idea of warped product manifolds was initiated by R. Blair D. Received Feb 6; Accepted Sep 8. He also has discussed the classification of CR-warped products in complex Euclidean [ 4 ], complex projective and complex hyperbolic spaces [ 5 ] which satisfy the equality case of the derived inequality. Plugging 8 into 7we have the following:. We assume that [ 19 ]. Inthe idea of warped product manifolds was initiated by R. Corresponding author.

Section 2, we recall the definition of a slant submanifold of an almost contact metric.

## SemiSlant Submanifolds of a Sasakian Manifold SpringerLink

Suppose now that M is a submanifold of a Sasakian manifold eM. Then. examples of slant submanifolds in the Sasakian-space-form R2m 1as the leaves of a We study slant submanifolds in K-contact manifolds and three- As we know, (α, β) - metrics defined by a Riemannian metric α and a 1-form β.

Video: Slant submanifolds in sasakian manifolds definition Manifolds 1.1 : Basic Definitions

slant submanifold of a 3-Sasakian manifold to be a slant submanifold. In Section 3, we define and characterize point-wise slant submanifolds of almost contact.

If the following inequality. Combining equations 10 and 11we arrive at. If the equality holds in 13then from 17 and the hypothesis of the theorem, we find that. Warped product bi-slant immersions in Kaehler manifolds.

Generalized inequalities on warped product submanifolds in nearly trans-Sasakin manifolds.

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Bishop and B. On the other hand, every nearly Sasakian manifold with dimension greater than five is a Sasakian manifold. For their geometric relations, see [ 12 ]. Gherghe C. |

We define and study both bi-slant and semi-slant submanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold.

## Geometric inequalities for warped product bislant submanifolds with a warping function

We prove a.

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This is assertion ii.

Bishop and B.

Slant submanifolds in sasakian manifolds definition |
I a Mat. Kodai Math. Blair D. Hence, our assertion ii is proved. This gives. |

Definition 1 [9] Let there exist three almost contact metric structures.

gated slant submanifolds of a Sasakian manifold [6]. N. Papaghiuc In his definition of pointwise slant submanifolds of almost contact metric. opment since B.-Y. Chen defined slant immersions in complex geometry as a slant submanifolds of K–contact and Sasakian manifolds and we have given sev.

Received Feb 6; Accepted Sep 8.

## A note on slant submanifolds of nearly transSasakian manifolds Mathematica Slovaca

Warped product bi-slant immersions in Kaehler manifolds. Contact Manifolds in Riemannian Geometry. Inspired by his work, many distinguished geometers have studied and obtained several sharp inequalities for warped product submanifolds in almost Hermitian manifolds and almost contact metric manifolds see the monograph [ 6 ] and the references therein.

Proof The proof of assertion i follows from Lemma 3. Lotta A. Uddin S.

Slant submanifolds in sasakian manifolds definition |
Papaghiuc N.
In order to prove assertion iiwe consider. Keywords: Nearly trans-Sasakian manifolds, Bi-slant submanifolds, Warped product bi-slant submanifolds. He also has discussed the classification of CR-warped products in complex Euclidean [ 4 ], complex projective and complex hyperbolic spaces [ 5 ] which satisfy the equality case of the derived inequality. Then we have. This completes the proof of the theorem. |

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Semi-slant submanifolds of a Sasakian manifold.

Generalized inequalities on warped product submanifolds in nearly trans-Sasakin manifolds.

Tripathi M.

This completes the proof of the theorem.