Pointwise almost h-semi-slant submanifolds

It was shown in [15,16] that there does not exist any warped product submanifold of a Kaehler manifold such that the spherical manifold of the warped product is proper slant. In this paper, we introduce the notion of warped product submanifolds with a slant function. We show that there exists a class of nontrivial warped product submanifolds of a Kaehler manifold such that the spherical manifold is pointwise slant by giving an example and a characterization theorem. We also prove that if the warped product is mixed totally geodesic then the warping function is constant.

show abstract

“…We also note that every slant submanifold is pointwise slant but converse may not be true. These submanifolds are also studied in [14].…”

Section: Introductionmentioning

confidence: 99%

Warped product submanifolds of Kaehler manifolds with pointwise slant fiber

Uddin

Stankovic

2018

Filomat

View full text Add to dashboard Cite

show abstract

“…The idea of pointwise semi-slant submanifolds as a natural generalization of CR-submanifolds of an almost Hermitian manifold in terms of a semi-slant function was defined and studied by Sahin [41] as follows: For some examples of pointwise semi-slant submanifold in a Kaehler manifold and related problems, we refer to [7,38,41].…”

Section: Preliminariesmentioning

confidence: 99%

Classification of warped product pointwise semi-slant submanifolds in complex space forms

Ali

Alkhaldi

Won

et al. 2019

Filomat

View full text Add to dashboard Cite

The main principle of this paper is to show that, a warped product pointwise semi-slant submanifold of type M n = N n 1 T × f N n 2 θ in a complex space form M 2m (c) admitting shrinking or steady gradient Ricci soliton, whose potential function is a well-define warped function, is an Einstein warped product pointwise semi-slant submanifold under extrinsic restrictions on the second fundamental form inequality attaining the equality in [4]. Moreover, under some geometric assumption, the connected and compactness with nonempty boundary are treated. In this case, we propose a necessary and sufficient condition in terms of Dirichlet energy function which show that a connected, compact warped product pointwise semi-slant submanifold of complex space forms must be a Riemannian product. As more applications, for the first one, we prove that M n is a trivial compact warped product, when the warping function exist the solution of PDE such as Euler-Lagrange equation. In the second one, by imposing boundary conditions, we derive a necessary and sufficient condition in terms of Ricci curvature, and prove that, a compact warped product pointwise semi-slant submanifold M n of a complex space form, is either a CRwarped product or just a usual Riemannian product manifold. We also discuss some obstructions to these constructions in more details.

show abstract

“…Almost complex submanifolds ( [1][2][3][4]), totally real submanifolds ( [5][6][7][8]), CR submanifolds ( [9][10][11][12]), QR submanifolds ( [13][14][15][16]), slant submanifolds (( [17][18][19][20][21][22]), pointwise slant submanifolds ( [23][24][25]), semi-slant submanifolds ( [26][27][28][29]), pointwise semi-slant submanifolds [30], pointwise almost h-slant submanifolds and pointwise almost h-semi-slant submanifolds [31], etc.…”

Section: Introductionmentioning

confidence: 99%

Pointwise Slant and Pointwise Semi-Slant Submanifolds in Almost Contact Metric Manifolds

Park

2020

Mathematics

View full text Add to dashboard Cite

In almost contact metric manifolds, we consider two kinds of submanifolds: pointwise slant, pointwise semi-slant. On these submanifolds of cosymplectic, Sasakian and Kenmotsu manifolds, we obtain characterizations and study their topological properties and distributions. We also give their examples. In particular, we obtain some inequalities consisting of a second fundamental form, a warping function and a semi-slant function.

show abstract

Pointwise almost h-semi-slant submanifolds

Cited by 24 publications

References 45 publications

Warped product submanifolds of Kaehler manifolds with pointwise slant fiber

Warped product submanifolds of Kaehler manifolds with pointwise slant fiber

Classification of warped product pointwise semi-slant submanifolds in complex space forms

Pointwise Slant and Pointwise Semi-Slant Submanifolds in Almost Contact Metric Manifolds

Contact Info

Product

Resources

About