Journal of the Tensor Society

Certain Cosmological Models of C-field with variable cosmological constant

RAM BHAROSHA TIWARI — Mon, 08 Jun 2026 09:17:55 +0000

A creation field cosmological model with variable cosmological constant is investigated in the framework of FRW space-time. We have taken into consideration that barotropic fluid is distributed throughout the universe in accordance with Hoyle and Narlikar [6]. To obtain the deterministic model, we assumed that Λ = 3α( ˙R^2 /R^2) +β( ¨R /R) , where R is the scaling factor. We find that while the creation field increases with time, the matter density remains constant due to the continuous production of new matter . Together with Λ ∼ 1/ t^2 , there is no particle horizon. In line with the findings of Riess et al. [24] and Perlmutter et al. [25], the model shows an expanding and accelerating universe.

Equivariant normal form for nondegenerate singular orbits pairs of restricted integrable Hamiltonian systems pairs on contact pairs.

Yatma MBODJI — Mon, 08 Jun 2026 09:18:03 +0000

On a differential manifold (M2h+2k+2, η, α) equipped to contact pair, we introduce the notion of
restricted completely integrable Hamiltonian system pair with (k +h) degrees of freedom whose first
integrals are invariant under the contact action of a compact Lie group G. We show that the singular
Legendrian foliation pair associated to this restricted completely integrable Hamiltonian system is
contact equivalent, in a G-equivariant way, to the linearised foliation pair in a neighbourhood of a
nondegenerate singular compact orbit pair.

LOCALLY SYMMETRIC CONDITION ON FOUR-DIMENSIONAL WALKER METRICS

Abdoul Salam Diallo, Mohamed Ayatola Dramé — Mon, 08 Jun 2026 09:18:25 +0000

The purpose of this paper is to investigate four-dimensional Walker manifolds. We establish conditions under which such manifolds are locally symmetric.

Ricci-Bourguignon Soliton on Quasi-Para Sasakian Manifolds

Prachi Mishra, Shravan Kumar Pandey — Mon, 08 Jun 2026 09:18:44 +0000

In the present article, we investigate Ricci–Bourguignon solitons on three-dimensional quasi-para-Sasakian manifolds equipped with a pseudo-Riemannian metric. We derive explicit conditions on the Ricci tensor under the assumption that the soliton potential vector field is affine conformal. It is shown that, in this setting, the Ricci tensor becomes a conformal quadratic Killing tensor. Furthermore, we prove that if the potential vector field is affine conformal, then it coincides with a Jacobi vector field along the geodesics generated by the Reeb vector field, and the Reeb vector field itself is geodesic. Finally, we establish that when the soliton vector field is conformal and the scalar curvature is harmonic, the manifold is Einstein and locally isometric to the three-dimensional hyperbolic space. These results highlight strong geometric rigidity phenomena for Ricci–Bourguignon solitons on quasi- para-Sasakian manifolds.

GENERALIZED Z-RECURRENT MANIFOLD WITH APPLICATIONS TO RELATIVITY

Giteshwari Pandey — Mon, 08 Jun 2026 09:18:10 +0000

In this paper, we investigate generalized Z-recurrent manifolds and explore their relevance in the context of relativity. Several geometric characteristics of generalized Z-recurrent space-times are examined under specific curvature constraints. Furthermore, we demonstrate that for a perfect fluid generalized recurrent space-time satisfying Einstein’s field equations without a cosmological constant, the Ricci tensor fulfills the time-like convergence condition. As a consequence, in such a matter-free space-time, the pressure of the fluid must be positive.