Slant Submanifolds of a Lorentz Kenmotsu Manifold

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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Slant and semi-slant submanifolds of a kenmotsu manifold

Mathematica Slovaca ◽

10.2478/s12175-007-0040-5 ◽

2007 ◽

Vol 57 (5) ◽

Cited By ~ 6

Author(s):

V. Khan ◽

M. Khan ◽

K. Khan

Keyword(s):

Present Note ◽

Kenmotsu Manifold ◽

Slant Submanifolds

AbstractIn the present note we have obtained some basic results pertaining to the geometry of slant and semi-slant submanifolds of a Kenmotsu manifold.

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Warped product skew CR-submanifolds of Kenmotsu manifolds and their applications

Filomat ◽

10.2298/fil1810505n ◽

2018 ◽

Vol 32 (10) ◽

pp. 3505-3528 ◽

Cited By ~ 2

Author(s):

Monia Naghi ◽

Ion Mihai ◽

Siraj Uddin ◽

Falleh Al-Solamy

Keyword(s):

Fundamental Form ◽

Warped Product ◽

Second Fundamental Form ◽

Warping Function ◽

Kenmotsu Manifold ◽

Slant Submanifolds ◽

The Second Fundamental Form ◽

Cr Submanifold ◽

Kenmotsu Manifolds ◽

Cr Submanifolds

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 bi-slant submanifolds of kenmotsu manifold

Asian-European Journal of Mathematics ◽

10.1142/s1793557122500619 ◽

2021 ◽

pp. 2250061

Author(s):

Sampa Pahan

Keyword(s):

Warped Product ◽

Slant Submanifold ◽

Kenmotsu Manifold ◽

Riemannian Product ◽

Slant Submanifolds

In this paper, we obtain several fundamental results of bi-slant submanifolds in a Kenmotsu manifold. Next, we give an example of such submanifolds. Later, we obtain some results of proper bi-slant submanifolds of a Kenmotsu manifold. Here, we show every warped product bi-slant submanifold of a Kenmotsu manifold to be a Riemannian product under some certain conditions.

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Another class ofwarped product skew CR-submanifolds of Kenmotsu manifolds

Filomat ◽

10.2298/fil1909583h ◽

2019 ◽

Vol 33 (9) ◽

pp. 2583-2600 ◽

Cited By ~ 1

Author(s):

Shyamal Hui ◽

Tanumoy Pal ◽

Joydeb Roy

Keyword(s):

Lower Bound ◽

Fundamental Form ◽

Warped Product ◽

Second Fundamental Form ◽

Warped Products ◽

Kenmotsu Manifold ◽

Equality Case ◽

Slant Submanifolds ◽

Kenmotsu Manifolds ◽

Two Factors

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.

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Contact pseudo-slant submanifolds of a Kenmotsu manifold

Journal of Mathematics and Computer Science ◽

10.22436/jmcs.016.03.08 ◽

2016 ◽

Vol 16 (03) ◽

pp. 386-394 ◽

Cited By ~ 1

Author(s):

Suleyman Dirik ◽

Mehmet Atceken ◽

Umit Yildirim

Keyword(s):

Kenmotsu Manifold ◽

Slant Submanifolds

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Classification of totally umbilical slant submanifolds of a Kenmotsu manifold

Filomat ◽

10.2298/fil1609405u ◽

2016 ◽

Vol 30 (9) ◽

pp. 2405-2412 ◽

Cited By ~ 1

Author(s):

Siraj Uddin ◽

Zafar Ahsan ◽

Yaakub Hadi

Keyword(s):

Mean Curvature ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Slant Submanifold ◽

Kenmotsu Manifold ◽

Totally Geodesic ◽

Totally Umbilical ◽

Slant Submanifolds ◽

The Mean

The purpose of this paper is to classify totally umbilical slant submanifolds of a Kenmotsu manifold. We prove that a totally umbilical slant submanifold M of a Kenmotsu manifold ?M is either invariant or anti-invariant or dimM = 1 or the mean curvature vector H of M lies in the invariant normal subbundle. Moreover, we find with an example that every totally umbilical proper slant submanifold is totally geodesic.

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Characterization theorems on warped product semi-slant submanifolds in Kenmotsu manifolds

Filomat ◽

10.2298/fil1913033a ◽

2019 ◽

Vol 33 (13) ◽

pp. 4033-4043 ◽

Cited By ~ 1

Author(s):

Akram Ali ◽

Siraj Uddin ◽

Ali Alkhaldi

Keyword(s):

Warped Product ◽

Tensor Fields ◽

Slant Submanifold ◽

Kenmotsu Manifold ◽

Slant Submanifolds ◽

Kenmotsu Manifolds ◽

Characterization Theorems

In this paper, we deal with the study of warped product semi-slant submanifolds isometrically immersed into a Kenmotsu manifold. We prove two characterization theorems for a warped product semi-slant submanifold in Kenmotsu manifolds in terms of the tensor fields.

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