Conharmonic Curvature Tensor Research Articles

Conharmonically flat and conharmonically symmetric warped product manifolds

This article presents characterizations of warped product manifolds based on the flatness and symmetry of the conharmonic curvature tensor. It is proved that when a warped product manifold is conharmonically flat, both the base and fiber manifolds exhibit constant sectional curvatures. In addition, the specific forms of the conharmonic curvature tensor are derived for both the base and fiber manifolds. It is demonstrated that in a conharmonically symmetric warped product manifold, the fiber manifold has a constant sectional curvature, while the base manifold is both Cartan-symmetric and conharmonically symmetric. In this scenario, the form of the conharmonic curvature tensor on the fiber manifold is determined. We characterize the generalized Robertson–Walker (GRW) space-time through the flatness and the symmetry of the conharmonic curvature tensor. It is shown that a conharmonically flat (symmetric) GRW space-time is a perfect fluid. Finally, a conharmonically flat standard static space-time is investigated.

On Z-Symmetric Manifold with Conharmonic Curvature Tensor in Special Conditions

The object of the present paper is to study the Z-symmetric manifold with conharmonic curvature tensor in special conditions. In this paper, we prove some theorems about these manifolds by using the properties of the Z-tensor.

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>

Proposed Theorems on the Lifts of Kenmotsu Manifolds Admitting a Non-Symmetric Non-Metric Connection (NSNMC) in the Tangent Bundle

The main aim of the proposed paper is to investigate the lifts of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We investigate several properties of the lifts of the curvature tensor, the conformal curvature tensor, and the conharmonic curvature tensor of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We also study and discover that the lift of the Kenmotsu manifold that admit NSNMC is regular in the tangent bundle. Additionally, we find that the data provided by the lift of Ricci soliton on the lift of Ricci semi-symmetric Kenmotsu manifold that admits NSNMC in the tangent bundle are expanding.

K- constant type Kahler and Nearly Kahler manifolds for conharmonic curvature tensor

The constant of permanence conharmonic type kahler and nearly kahler manifold conditions are obtained when the Nearly Kahler manifold is a manifold conharmonic constant type (K). and also proved that M nearly kahler manifold of pointwise constant holomorphic sectional conharmonic (PHKm(X)) – curvature) curvature tensor if the components of holomorphic sectional (HS- curvature) curvature tensor in the adjoint G-structure space that satisfies condition .

The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures

This paper aims to study some semi-symmetric and curvature tensor conditions on α-Kenmotsu pseudo-metric manifolds. Some conditions of semi-symmetric, locally symmetric, and the Ricci semi-symmetric are considered on such manifolds. Also, the relationships between the M-projective curvature tensor and conformal curvature tensor, concircularly curvature tensor, and conharmonic curvature tensor are investigated. Finally, an example of α-Kenmotsu pseudo-metric structure is given.

The Properties of Projective, Concircular and Conharmonic Curvature Tensor Fields on a Complex Sasakian Manifold

In this article, the properties of projective, concircular and conharmonic curvature tensor fields on a complex Sasakian manifold are investigated.

Some geometric and physical properties of pseudo ψ-conharmonically symmetric manifolds

In this article, we present a new tensor that generalizes the conharmonic curvature tensor, termed the ψ-conharmonic curvature tensor. In the first part, we derive some fundamental geometrical properties of a pseudo ψ-conharmonically symmetric manifold (briefly, ) and give some fascinating outcomes. Among others, we establish that an Einstein manifold is of zero scalar curvature. Besides, we investigate ψ-conharmonically flat perfect fluid and spacetimes, respectively. As a result, we acquire some significant theorems. Finally, we construct several non-trivial examples to establish the existence of .

Conharmonic Curvature Inheritance in Spacetime of General Relativity

The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV.

How a projectively flat geometry regulates F(R)-gravity theory?

In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.

LP-Sasakian Manifolds Equipped with Zamkovoy Connection and Conharmonic Curvature Tensor

In this paper we have proved some results on conharmonically flat, quasi conharmonically flat and φ-conharmonically flat LP-Sasakian manifolds with respect to Zamkovoy connection. Also, we study generalized conharmonic φ-recurrent LP-Sasakian manifolds with respect to Zamkovoy connection. Moreover, we study LP-Sasakian manifolds satisfying K*(ξ,U)∘R*=0, where K* denotes conharmonic curvature tensor and R* denotes Riemannian curvature tensor with respect to Zamkovoy connection.

Conharmonic curvature tensor on nearly cosymplectic manifolds with generalized tanaka-webster connection

Conharmonic curvature tensor on nearly cosymplectic manifolds with generalized tanaka-webster connection

On Anti-Kähler manifolds with complex semi-symmetric metric $F-$connection

In this paper, we construct a complex semi-symmetric metric $F$-connection on an anti-Kähler manifold. First, we present some results concerning the torsion tensor of the complex semi-symmetric metric $F$-connection. Finally, we find expressions of the curvature tensor, the conharmonic curvature tensor and the Weyl projective curvature tensor of such connection, and study their properties.

Certain curvature properties of N(k)-quasi Einstein manifolds

In this paper, we consider N(k)-quasi Einstein manifolds satisfying the curvature conditions P¯(ξ,X)⋅W2=0 and P¯(ξ,X)·H=0 where P¯, W2 and H are the pseudo projective, W2 and conharmonic curvature tensors respectively. We study pseudo projectively symmetric N(k)-quasi Einstein manifolds and show that there does not exist a pseudo projectively semisymmetric N(k)-quasi Einstein manifold. Also, we construct some examples to support the existence of such manifolds.

Certain results on the conharmonic curvature tensor of (κ, μ)-contact metric manifolds

The paper presents a study of \( (\kappa,\mu) \)-contact metric manifolds satisfying certain conditions on the conharmonic curvature tensor.

On harmonicity and Miao–Tam critical metrics in a perfect fluid spacetime

The curvature properties of a perfect fluid spacetime have been studied when the Riemann curvature, the projective curvature, the concircular curvature, the conformal curvature and the conharmonic curvature tensors are, respectively, harmonic. In the flatness case, if the velocity vector of the fluid is torse-forming, we can completely characterize it. Also, we study the consequences of the existence of $$\eta $$ -Einstein, $$\eta $$ -Ricci and $$\eta $$ -Yamabe solitons in perfect fluid spacetime satisfying Miao–Tam critical metric condition.

The Concircular Curvature Tensor Of The Locally Conformal Kahler Manifold

In this research, we are calculated components conharmonic curvature tensor in some aspects Hermeation manifolding in particular of the Locally Conformal Kahler manifold. And we prove that this tensor possesses the classical symmetry properties of the Riemannian curvature. They also, establish relationships between the components of the tensor in this manifold.

ON VIASMAN-GRAY MANIFOLD WITH GENERALIZED CONHARMONIC CURVATURE TENSOR

The current study deals with generalized conhormonic ensor of Vaisman - Gray manifold. The aim of this paper to calculate components generalized Ricci tensor and generalized Riemannian tensor of - adjoint -s to find Generalized conharmonic Curvature tensor of -manifold, one of the an manifold struc es is donated , w re a d re ely de o the near hler m old an ally conformal kahler m fold have been studied

η-Einstein nearly Kenmotsu manifolds

In this paper, we showed that an [Formula: see text]-Einstein nearly Kenmotsu manifold with projective curvature tensor [Formula: see text], and conharmonic curvature tensor [Formula: see text], satisfy the conditions [Formula: see text] and [Formula: see text], respectively. Furthermore, we obtain scalar curvature of a projectively flat and a conharmonically flat [Formula: see text]-Einstein nearly Kenmotsu manifold.

A study on complex semi-symmetric non-metric F-connections on anti-Kähler manifolds

In this paper, we have considered an anti-Kahler manifold (M, g, F) admitting a complex semi-symmetric non-metric F-connection $${\widetilde{\nabla }}$$ . First we study the properties of the curvature tensor, the conharmonic curvature tensor and the conformal curvature tensor of the connection $${\widetilde{\nabla }}$$ . Also, we investigate the condition for the anti-Kahler manifold (M, g, F) to be Einstein space with respect to the connection $${\widetilde{\nabla }}$$ . Finally, we define the dual connection of the connection $${\widetilde{\nabla }}$$ and present some results related to its curvature tensors.