Contact CR-Warped Product Submanifolds in Sasakian Manifolds

Hasegawa, Izumi; Iordache, Mihai

doi:10.1023/b:geom.0000006582.29685.22

Cited by 112 publications

(108 citation statements)

References 7 publications

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“…B. Y. Chen [6] initiated the study by exploring CR-submanifolds as warped products in a Kaehler manifold. I. Hasegawa and I. Mihai [7] extended the study by investigating contact CR-submanifolds as warped product submanifolds in Sasakian manifolds. They proved that warped product contact CR-submanifolds N ⊥ × f N T in Sasakian manifolds are trivial, i.e.…”

Section: Introductionmentioning

confidence: 99%

A note on warped product submanifolds of Kenmotsu manifolds

Khan

Uddin

2011

Mathematica Slovaca

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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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Section: Introductionmentioning

confidence: 99%

A note on warped product submanifolds of Kenmotsu manifolds

Khan

Uddin

2011

Mathematica Slovaca

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“…Since [X, V ] =, by using (8) we have ⊥ is anti-invariant with respect to φ. A submanifold M of a Sasakian manifoldM is called contact CR-warped product [10] if it is the warped product M T × f M ⊥ of an invariant submanifold M T tangent to ξ and a C-totally real submanifold M ⊥ ofM . For a contact CR-warped product submanifold of a Sasakian manifold, Hasegawa and Mihai proved the following formula.…”

Section: Preliminariesmentioning

confidence: 99%

“…The notion of contact CRwarped product submanifolds of a Sasakian manifold was defined by Hasegawa and Mihai in [10] and they showed that the only warped products with nonconstant warping function which are contact CR-submanifolds in a Sasakian manifoldM have the form M = M T × f M ⊥ with M T an invariant submanifold tangent to the characteristic vector field ξ and M ⊥ a C-totally real submanifold ofM . They simply called such submanifolds contact CR-warped products.…”

Section: Introductionmentioning

confidence: 99%

Homology of Contact Cr-Warped Product Submanifolds of an Odd-Dimensional Unit Sphere

Şahin¹,

Şahin²

2015

Bulletin of the Korean Mathematical Society

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“…After that, many researchers extended this idea for other structures on a Riemannian manifold (some of them are cited here [8,14]). For the survey on warped product submanifolds, we refer to [6,7].…”

Section: Introductionmentioning

confidence: 99%

Another class of warped product CR-submanifolds in Kenmotsu manifolds

Uddin¹,

Alghanemi²,

Naghi³

et al. 2017

J. Math. Computer Sci.

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Recently, Arslan et al. [K. Arslan, R. Ezentas, I. Mihai, C. Murathan, J. Korean Math. Soc., 42 (2005), 1101-1110] studied contact CR-warped product submanifolds of the form M T × f M ⊥ of a Kenmotsu manifold M, where M T and M ⊥ are invariant and anti-invariant submanifolds of M, respectively. In this paper, we study the warped product submanifolds by reversing these two factors, i.e., the warped products of the form M ⊥ × f M T which have not been considered in earlier studies. On the existence of such warped products, a characterization is given. A sharp estimation for the squared norm of the second fundamental form is obtained, and in the statement of inequality, the equality case is considered. Finally, we provide two examples of non-trivial warped product submanifolds.

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Contact CR-Warped Product Submanifolds in Sasakian Manifolds

Cited by 112 publications

References 7 publications

A note on warped product submanifolds of Kenmotsu manifolds

A note on warped product submanifolds of Kenmotsu manifolds

Homology of Contact Cr-Warped Product Submanifolds of an Odd-Dimensional Unit Sphere

Another class of warped product CR-submanifolds in Kenmotsu manifolds

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