Another class of warped product CR-submanifolds in Kenmotsu manifolds

In this paper, we introduce the notion of warped product skew CR-submanifolds in Kenmotsu manifolds. We obtain several results on such submanifolds. A characterization for skew CR-submanifolds is obtained. Furthermore, we establish an inequality for the squared norm of the second fundamental form of a warped product skew CR-submanifold M1 x fM? of order 1 in a Kenmotsu manifold ?M in terms of the warping function such that M1 = MT x M?, where MT, M? and M? are invariant, anti-invariant and proper slant submanifolds of ?M, respectively. Finally, some applications of our results are given.

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Warped product CR-submanifolds of Lorentzian β-Kenmotsu manifolds

Publications de l Institut Mathematique ◽

10.2298/pim1206157u ◽

2012 ◽

Vol 92 (106) ◽

pp. 157-163

Author(s):

Siraj Uddin ◽

Cenap Ozel ◽

Azam Khan

Keyword(s):

Warped Product ◽

Warped Products ◽

Characterization Result ◽

Kenmotsu Manifolds ◽

Cr Submanifolds

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

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Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽

10.2298/fil1718833k ◽

2017 ◽

Vol 31 (18) ◽

pp. 5833-5853 ◽

Cited By ~ 1

Author(s):

Viqar Khan ◽

Mohammad Shuaib

Keyword(s):

Present Article ◽

Warped Product ◽

Shape Operator ◽

Warped Products ◽

Canonical Structure ◽

Slant Submanifold ◽

Kenmotsu Manifold ◽

Slant Submanifolds ◽

Kenmotsu Manifolds

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.

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Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold

Mathematica Slovaca ◽

10.1515/ms-2017-0340 ◽

2020 ◽

Vol 70 (1) ◽

pp. 151-160

Author(s):

Amalendu Ghosh

Keyword(s):

Scalar Curvature ◽

Warped Product ◽

Constant Scalar Curvature ◽

Product Structure ◽

Kenmotsu Manifold ◽

Kenmotsu Manifolds ◽

Almost Kenmotsu Manifolds ◽

Yamabe Soliton

AbstractIn this paper, we study Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold. First, we prove that if a Kenmotsu metric is a Yamabe soliton, then it has constant scalar curvature. Examples has been provided on a larger class of almost Kenmotsu manifolds, known as β-Kenmotsu manifold. Next, we study quasi Yamabe soliton on a complete Kenmotsu manifold M and proved that it has warped product structure with constant scalar curvature in a region Σ where ∣Df∣ ≠ 0.

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Warped product CR-submanifolds of Sasakian manifolds with respect to certain connections

Journal of the Indonesian Mathematical Society ◽

10.22342/jims.25.3.765.194-202 ◽

2019 ◽

Vol 25 (3) ◽

pp. 194-202

Author(s):

Shyamal Kumar Hui ◽

Joydeb Roy

Keyword(s):

Warped Product ◽

Ricci Solitons ◽

Sasakian Manifolds ◽

Metric Connection ◽

Cr Submanifolds

The present paper deals with the study of warped product CR-submanifolds of Sasakian manifolds with respect to semisymmetric metric and semisymmetric non-metric connection. Among others, Ricci solitons of such notions have been investigated.

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On warped product bi-slant submanifolds of Kenmotsu manifolds

Arab Journal of Mathematical Sciences ◽

10.1016/j.ajmsc.2019.06.001 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Siraj Uddin ◽

Ion Mihai ◽

Adela Mihai

Keyword(s):

Fundamental Form ◽

Warped Product ◽

Second Fundamental Form ◽

Warping Function ◽

Equality Case ◽

General Inequality ◽

Kaehler Manifolds ◽

Slant Submanifolds ◽

The Second Fundamental Form ◽

Kenmotsu Manifolds

Chen (2001) initiated the study of CR-warped product submanifolds in Kaehler manifolds and established a general inequality between an intrinsic invariant (the warping function) and an extrinsic invariant (second fundamental form).In this paper, we establish a relationship for the squared norm of the second fundamental form (an extrinsic invariant) of warped product bi-slant submanifolds of Kenmotsu manifolds in terms of the warping function (an intrinsic invariant) and bi-slant angles. The equality case is also considered. Some applications of derived inequality are given.

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