Einstein doubly warped product manifolds with semi-symmetric metric connection

Class A ◽

Warped Product Manifold ◽

Metric Connection ◽

In this paper, we study the doubly warped product manifolds with semi-symmetric metric connection. We derive the curvature formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of components of doubly warped product manifolds. We also prove the necessary and sufficient condition for a doubly warped product manifold to be a warped product manifold. We obtain some results for an Einstein doubly warped product manifold and Einstein-like doubly warped product manifold of class A with respect to a semi-symmetric metric connection.

A note on warped product almost quasi-Yamabe solitons

Filomat ◽

10.2298/fil1907009b ◽

2019 ◽

Vol 33 (7) ◽

pp. 2009-2016 ◽

Cited By ~ 5

Author(s):

Adara Blaga

Keyword(s):

Riemannian Manifolds ◽

Warped Product ◽

Sufficient Conditions ◽

Constant Scalar Curvature ◽

Product Manifold ◽

Base Manifold ◽

Warped Product Manifold ◽

Yamabe Solitons ◽

Yamabe Soliton

We consider almost quasi-Yamabe solitons in Riemannian manifolds, derive a Bochner-type formula in the gradient case and prove that under certain assumptions, the manifold is of constant scalar curvature. We also provide necessary and sufficient conditions for a gradient almost quasi-Yamabe soliton on the base manifold to induce a gradient almost quasi-Yamabe soliton on the warped product manifold.

Radical screen transversal lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781850024x ◽

2018 ◽

Vol 15 (02) ◽

pp. 1850024

Author(s):

Garima Gupta ◽

Rakesh Kumar ◽

Rakesh Kumar Nagaich

Keyword(s):

Product Manifold ◽

Kaehler Manifold ◽

Screen Distribution ◽

Kaehler Manifolds ◽

Metric Connection ◽

Characterization Theorems ◽

Lightlike Submanifolds ◽

Lightlike Submanifold

We study radical screen transversal ([Formula: see text])-lightlike submanifolds of an indefinite Kaehler manifold admitting a quarter-symmetric non-metric connection and obtain a necessary and sufficient condition for the screen distribution of a radical [Formula: see text]-lightlike submanifold to be integrable. We also study totally umbilical radical [Formula: see text]-lightlike submanifolds and obtain some characterization theorems for a radical [Formula: see text]-lightlike submanifold to be a lightlike product manifold. Finally, we establish some results regarding the vanishes of null sectional curvature.

NATURAL CONNECTION WITH TOTALLY SKEW-SYMMETRIC TORSION ON RIEMANNIAN ALMOST PRODUCT MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781250003x ◽

2012 ◽

Vol 09 (01) ◽

pp. 1250003 ◽

Cited By ~ 2

Author(s):

DIMITAR MEKEROV ◽

MANCHO MANEV

Keyword(s):

Linear Connection ◽

Riemannian Metric ◽

Sufficient Condition ◽

Product Manifold ◽

Natural Connection ◽

Almost Product Manifold ◽

Hermitian Geometry ◽

Levi Civita Connection ◽

On a Riemannian almost product manifold (M, P, g), we consider a linear connection preserving the almost product structure P and the Riemannian metric g and having a totally skew-symmetric torsion. We determine the class of the manifolds (M, P, g) admitting such a connection and prove that this connection is unique in terms of the covariant derivative of P with respect to the Levi-Civita connection. We find a necessary and sufficient condition the curvature tensor of the considered connection to have similar properties like the ones of the Kähler tensor in Hermitian geometry. We pay attention to the case when the torsion of the connection is parallel. We consider this connection on a Riemannian almost product manifold (G, P, g) constructed by a Lie group G.

Lower bounds of generalised normalised δ- Casorati curvature for real hypersurfaces in complex quadric endowed with semi-symmetric metric connection

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.50.2019.2909 ◽

2018 ◽

Vol 50 (2) ◽

pp. 187-198 ◽

Cited By ~ 1

Author(s):

Pooja Bansal ◽

Mohammad Hasan Shahid

Keyword(s):

Lower Bounds ◽

Real Hypersurfaces ◽

Sufficient Condition ◽

Complex Quadric ◽

Metric Connection ◽

Casorati Curvature

The main intention of the present paper is to develop two extremal inequalities involving normalized δ-Casorati curvature and extrinsic generalised normalised δ-Casorati curvature for real hypersurfaces in complex quadric Qm admitting semi-symmetric metric connection. Further, we derive the necessary and sufficient condition for the equality in both cases

Biwarped product submanifolds of a Kähler manifold

Filomat ◽

10.2298/fil1807349t ◽

2018 ◽

Vol 32 (7) ◽

pp. 2349-2365 ◽

Cited By ~ 2

Author(s):

Hakan Taştan

Keyword(s):

Fundamental Form ◽

Warped Product ◽

Kähler Manifold ◽

Second Fundamental Form ◽

Sufficient Condition ◽

Equality Case ◽

The Second Fundamental Form ◽

Special Cases ◽

We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in K?hler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a non-trivial biwarped product submanifold of a certain type by giving an illustrate example. We also give a necessary and sufficient condition for such submanifolds to be locally trivial. Moreover, we establish an inequality for the squared norm of the second fundamental form in terms of the warping functions for such submanifolds. The equality case is also discussed.

Geometry of semi-transversal lightlike warped product submanifolds of indefinite Kaehler manifolds

Asian-European Journal of Mathematics ◽

10.1142/s1793557121500017 ◽

2019 ◽

pp. 2150001

Author(s):

Sangeet Kumar

Keyword(s):

Warped Product ◽

Shape Operator ◽

Sufficient Condition ◽

Kaehler Manifold ◽

Type Formula ◽

Kaehler Manifolds ◽

Lightlike Submanifolds ◽

Lightlike Submanifold

In this paper, we investigate warped product semi-transversal lightlike submanifolds of indefinite Kaehler manifolds. It is shown that there does not exist any warped product semi-transversal lightlike submanifold of the type [Formula: see text] in an indefinite Kaehler manifold. Moreover, a necessary and sufficient condition for an isometrically immersed semi-transversal lightlike submanifold of an indefinite Kaehler manifold to be a semi-transversal lightlike warped product of the type [Formula: see text] is obtained, in terms of the shape operator.

Geometric aspects of CR-warped product submanifolds of T-manifolds

Asian-European Journal of Mathematics ◽

10.1142/s179355711750067x ◽

2017 ◽

Vol 10 (04) ◽

pp. 1750067

Author(s):

Akram Ali ◽

Wan Ainun Mior Othman

Keyword(s):

Warped Product ◽

Characterization Theorem ◽

Second Fundamental Form ◽

Warping Function ◽

Sufficient Condition ◽

Warped Products ◽

Space Forms ◽

The Second Fundamental Form ◽

In this paper, we study CR-warped product submanifolds of [Formula: see text]-manifolds. We prove that the CR-warped product submanifolds with invariant fiber are trivial warped products and provide a characterization theorem of CR-warped products with anti-invariant fiber of [Formula: see text]-manifolds. Moreover, we develop an inequality of CR-warped product submanifolds for the second fundamental form in terms of warping function and the equality cases are considered. Also, we find a necessary and sufficient condition for compact oriented CR-warped products turning into CR-products of [Formula: see text]-space forms.

Remarks on metallic warped product manifolds

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1802269b ◽

2018 ◽

Vol 33 (2) ◽

pp. 269

Author(s):

Adara-Monica Blaga ◽

Cristina-Elena Hretcanu

Keyword(s):

Riemannian Manifold ◽

Riemannian Manifolds ◽

Warped Product ◽

Sufficient Condition ◽

Metallic Structure ◽

We characterize the metallic structure on the product of two metallic manifolds in terms of metallic maps and provide a necessary and sufficient condition for the warped product of two locally metallic Riemannian manifolds to be locally metallic. The particular case of product manifolds is discussed and an example of metallic warped product Riemannian manifold is provided.

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

Filomat ◽

10.2298/fil1916273a ◽

2019 ◽

Vol 33 (16) ◽

pp. 5273-5290

Author(s):

Akram Ali ◽

Ali Alkhaldi ◽

Jae Lee ◽

Wan Othman

Keyword(s):

Warped Product ◽

Complex Space ◽

Space Form ◽

Sufficient Condition ◽

Slant Submanifold ◽

Space Forms ◽

Riemannian Product ◽

Complex Space Forms

The main principle of this paper is to show that, a warped product pointwise semi-slant submanifold of type Mn = Nn1 T xf Nn2? in a complex space form ?M2m (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 Mn 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 Mn of a complex space form, is either a CR warped product or just a usual Riemannian product manifold. We also discuss some obstructions to these constructions in more details.