B.-Y. Chen’s Inequality for Bi-warped Products and Its Applications in Kenmotsu manifolds

Author(s):  
Siraj Uddin ◽  
Falleh R. Al-Solamy ◽  
Mohammad Hasan Shahid ◽  
Amani Saloom
Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.


2019 ◽  
Author(s):  
Monia Fouad Naghi ◽  
Siraj Uddin ◽  
Mića S. Stanković

2012 ◽  
Vol 92 (106) ◽  
pp. 157-163
Author(s):  
Siraj Uddin ◽  
Cenap Ozel ◽  
Azam Khan

We study the geometry of warped product submanifolds of Lorentzian ?-Kenmotsu manifolds. We obtain a characterization result for CR-warped products.


Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2583-2600 ◽  
Author(s):  
Shyamal Hui ◽  
Tanumoy Pal ◽  
Joydeb Roy

Recently, Naghi et al. [32] studied warped product skew CR-submanifold of the form M1 xf M? of order 1 of a Kenmotsu manifold ?M such that M1 = MT x M?, where MT, M? and M? are invariant, anti-invariant and proper slant submanifolds of ?M. The present paper deals with the study of warped product submanifolds by interchanging the two factors MT and M?, i.e, the warped products of the form M2 xf MT such that M2 = M? x M?. The existence of such warped product is ensured by an example and then we characterize such warped product submanifold. A lower bound of the squared norm of second fundamental form is derived with sharp relation, whose equality case is also considered.


Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4721-4731
Author(s):  
Siraj Uddin ◽  
Monia Naghi

In this paper, we study warped products of contact skew-CR submanifolds, called contact skew CR-warped products in Kenmotsu manifolds. We obtain a lower bound relationship between the squared norm of the second fundamental form and the warping function. Furthermore, the equality case is investigated and some applications of derived inequality are given.


2018 ◽  
Vol 48 (1) ◽  
pp. 47-60
Author(s):  
Pradip Majhi ◽  
Ajit Barman ◽  
Uday Chand De
Keyword(s):  

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.


Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6211-6218 ◽  
Author(s):  
Young Suh ◽  
Krishanu Mandal ◽  
Uday De

The present paper deals with invariant submanifolds of CR-integrable almost Kenmotsu manifolds. Among others it is proved that every invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold with k < -1 is totally geodesic. Finally, we construct an example of an invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold which is totally geodesic.


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