Kenmotsu Manifolds Research Articles

Non-existence of proper η-Einstein Kenmotsu manifolds

Non-existence of proper η-Einstein Kenmotsu manifolds

On warped product pointwise quasi bi-slant submanifolds of Kenmotsu manifolds

On warped product pointwise quasi bi-slant submanifolds of Kenmotsu manifolds

A Study of $\phi$-Pluriharmonicity in Quasi bi-slant Conformal $\xi^\perp$-Submersions From Kenmotsu Manifold

In the present research paper, we look into quasi bi-slant conformal $\xi^{\perp}$-submersions from Kenmotsu manifolds onto Riemannian manifolds as a generalisation of quasi hemi-slant conformal submersions. We investigate the geometry of distributions's leaves in order to explain integrability conditions for distributions. Furthermore, we study of certain decomposition theorems, additionaly provide non-trivial examples of quasi bi-slant conformal $\xi^{\perp}$-submersions from Kenmotsu manifolds. We also look at the $\phi$-pluriharmonicity of quasi bi-slant conformal $\xi^{\perp}$-submersions.

Semi-symmetric types on hyperbolic Kenmotsu manifolds

In this paper, we give some necessary conditions for an hyperbolic Kenmotsu manifolds M satisfying semi-symmetric, Ricci semi-symmetric, Weyl semi-symmetric and Einstein semi-symmetric. Next, we study the notion of n-Ricci soliton in context of hyperbolic Kenmotsu 3-manifolds M3 and we construct an example to illustrate the existence of n-Ricci soliton. Finally, we present some conditions to M admitting Codazzi type of Ricci tensor and cyclic n-recurrent Ricci tensor.

On the geometry of semi-slant submanifolds of a conformal Kenmotsu manifold

Abstract The object of this paper is to conduct an in-depth examination of semi-slant submanifolds within the framework of a conformal Kenmotsu manifolds. Our investigation is centered around identifying and understanding the conditions that ensure the integrability of both invariant and slant distributions, which play a pivotal role in defining semi-slant submanifolds. Additionally, we prove some interesting results for semi-slant submanifolds with parallel canonical structures.

Some Properties of Kenmotsu Manifolds Admitting a New Type of Semi-Symmetric Non-Metric Connection

Some Properties of Kenmotsu Manifolds Admitting a New Type of Semi-Symmetric Non-Metric Connection

Almost η-Ricci solitons on two classes of almost Kenmotsu manifolds

The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting almost η-Ricci solitons. In this context, we have shown that in a (k, µ) and (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton the curvature conditions (i) the manifold is Einstein, (ii) the manifold is Ricci symmetric (∇S = 0), (iii) the manifold is Ricci semisymmetric (R · S = 0) and (iv) the manifold is projective Ricci semisymmetric (P · S = 0) are equivalent. Also, we have shown that the curvature condition Q · P = 0 in a (k, µ)-almost Kenmotsu manifold admitting an almost η-Ricci soliton holds if and only if the manifold is locally isometric to the hyperbolic space H2n+1(−1) and if a (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton satisfies the curvature condition Q · R = 0, then it is locally isometric to the Riemannian product H n+1(−4) × ℝn. n.

An optimized Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms

In this paper, we present necessary and sufficient conditions for a Lorentz contact manifold to be a Lorentz Kenmotsu manifold. Moreover, we obtain the optimal Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms. Furthermore, the equality case of Chen inequality has been discussed.

LP-Kenmotsu manifolds admitting Bach almost solitons

For an $LP$-Kenmotsu manifold of dimension $m$ (briefly, ${(LPK)_{m}}$) admitting Bach almost solitons $(g,\zeta,\lambda)$, we have explored the characteristics of norm of Ricci operator. Besides, we have studied the Bach tensor on Lorentzian para-Kenmotsu manifolds to have an $\eta$-Einstein manifold. Afterwards, we have proved that Bach almost solitons $(g,\zeta,\lambda)$ are always steady when, a Lorentzian para-Kenmotsu manifold of dimension-three has Bach almost solitons.

∗-CONFORMAL CURVATURE OF CONTACT METRIC MANIFOLDS

We introduce the ∗-conformal curvature tensor and ∗η-Einstien manifolds in contact manifolds. We investigate this tensor in the three main classes of contact manifolds: Sasakian manifolds, Kenmotsu manifolds, and cosymplectic manifolds. We prove that a manifold is η-Einstienian if and only if be ∗η-Einstienian manifold.

Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

On Generalized Kenmotsu Manifolds as Hypersurfaces of Vaisman-Gray Manifolds

In this paper, we conclude that the hypersurfaces of Vaisman-Gray manifolds have generalized Kenmotsu structures under some conditions for the Lee form, Kirichenko's tensors and the second fundamental form of the immersion of the hypersurface into the manifold of Vaisman-Gray class. Moreover, the components of the second fundamental form are determined when the foregoing hypersurfaces have generalized Kenmotsu structures or any special kind of it or Kenmotsu structures, such that some of these components are vanish. Also, some components of Lee form and some components of some Kirichenko's tensors in the Vaisman--Gray class are equal to zero. On the other hand, the minimality of totally umbilical, totally geodesic hypersurfaces of Vaisman--Gray manifolds with generalized Kenmotsu structures are investigated. In addition, we deduced that the hypersurface of Vaisman--Gray manifold that have generalized Kenmotsu structure is totally geodesic if and only if it is totally umbilical and some components of Lee form are constants.

HYPERBOLIC KENMOTSU MANIFOLD ADMITTING A NEW TYPE OF SEMI-SYMMETRIC NON-METRIC CONNECTION

In this work, we study a new type of semi-symmetric non-metric connection on hyperbolic Kenmotsu manifold. Some Riemannian curvature’s characteristics on hyperbolic Kenmotsu manifold are investigated. The properties of semi-symmetric, locally ϕ-symmetric and Ricci semi-symmetric hyperbolic Kenmotsu manifold endowed with a new type of semi-symmetric nonmetric connection are evaluated. A semi-symmetric and Ricci semi-symmetric hyperbolic Kenmotsu manifold with a semi-symmetric non-metric connection is also demonstrated, the Ricci soliton of data (g1,ξ,λ) is shrinking. Finally, we demonstrate our results with a 3-dimensional example.

Generalized B-curvature tensor within the framework of Lorentzian β-Kenmotsu manifold

The objective of this paper is to study some curvature properties of generalized [Formula: see text]-curvature tensor on Lorentzian [Formula: see text]-Kenmotsu manifold. Here first, we describe certain vanishing properties of generalized [Formula: see text]-curvature tensor on Lorentzian [Formula: see text]-Kenmotsu manifold and obtained several interesting results. Next, we formulate [Formula: see text] semi-symmetric condition on Lorentzian [Formula: see text]-Kenmotsu manifold. Again, we discussed the generalized [Formula: see text] pseudo-symmetric condition on Lorentzian [Formula: see text]-Kenmotsu manifold. We also characterized generalized [Formula: see text] [Formula: see text]-recurrent Lorentzian [Formula: see text]-Kenmotsu manifold. Further, we deal with Lorentzian [Formula: see text]-Kenmotsu manifold satisfying [Formula: see text] condition.

Certain results on tangent bundle endowed with generalized Tanaka Webster connection (GTWC) on Kenmotsu manifolds

<p>This work studies the complete lifts of Kenmotsu manifolds associated with the generalized Tanaka-Webster connection (GTWC) in the tangent bundle. Using the GTWC, this study explores the complete lifts of various curvature tensors and geometric structures from Kenmotsu manifolds to their tangent bundles. Specifically, it examines the complete lifts of Ricci semi-symmetry, the projective curvature tensor, $ \Phi $-projectively semi-symmetric structures, the conharmonic curvature tensor, the concircular curvature tensor, and the Weyl conformal curvature tensor. Additionally, the research delves into the complete lifts of Ricci solitons on Kenmotsu manifolds with the GTWC within the tangent bundle framework, providing new insights into their geometric properties and symmetries in the lifted space. The data on the complete lifts of the Ricci soliton in Kenmotsu manifolds associated with the GTWC in the tangent bundle are also investigated. An example of the complete lifts of a $ 5 $-dimensional Kenmotsu manifold is also included.</p>

Geometry of sub - Riemannian manifolds equipped with a semimetric quarter - symmetric connection

On a sub-Riemannian manifold we introduce a semimetric quarter-symmetric connection by defining intrinsic metric connection and two structural endomorphisms preserving the distribution on a sub-Riemannian manifold. We find conditions ensuring the metric property of the introduced connection. We clarify the nature of the structural endomorphisms of semimetric connection consistent with a sub-Riemannian quasi-static structure defined on non-holonomic Kenmotsu manifold and on almost quasi-Sasakian manifold. We find conditions, under which the mentioned manifolds are Einstein manifolds with respect to the quarter-symmetric connection.

Pseudoparallel invariant submanifolds of Kenmotsu manifolds

In this paper, we consider pseudoparallel invariant submanifolds, a particular class of invariant submanifolds of Kenmotsu manifolds, on $W_8$ curvature tensor and investigate some of their basic characterizations, such as $W_8$ pseudoparallel, $W_8$-2 pseudoparallel, $W_8$-Ricci generalized pseudoparallel, and $W_8$-2 Ricci generalized pseudoparallel. Moreover, we present some relations between these pseudoparallel invariant submanifolds and semi-parallel invariant submanifolds. We finally discuss the need for further research.

Geometry of almost contact metrics as almost ∗-Ricci solitons

In this paper, we give some characterizations by considering ∗-Ricci soliton as a Kenmotsu metric. We prove that if a Kenmotsu manifold represents an almost ∗-Ricci soliton and the potential vector field [Formula: see text] is a Jacobi along the Reeb vector field, then it is a steady ∗-Ricci soliton. Next, we show that a Kenmotsu matric endowed an almost ∗-Ricci soliton which is Einstein metric if it is [Formula: see text]-Einstein or the potential vector field [Formula: see text] is collinear to the Reeb vector field or [Formula: see text] is an infinitesimal contact transformation.

CSI-ξ^⊥-Riemannian maps from Kenmotsu manifolds to Riemannian manifolds

In this article, we take into account a new class of semi-invariant ξ⊥-Riemannian maps, namely, CSI-ξ⊥ (Clairaut semi-invariant-ξ⊥)-Riemannian maps in contact geometry and discuss CSI-ξ⊥-Riemannian maps from Kenmotsu manifolds to Riemannian manifolds. We extend the notion of semi-invariant ξ⊥-Riemannian maps to CSI-ξ⊥-Riemannian maps and obtain a necessary and sufficient condition for this extension. We also investigate some geometric properties of these maps and exhibit a non-trivial example of discussed maps.

On Two Different Classes of Warped Product Submanifolds of Kenmotsu Manifolds

On Two Different Classes of Warped Product Submanifolds of Kenmotsu Manifolds