Journal of the Tensor Society

EXPLICIT CHARACTERIZATION OF THE RADIUS OF CURVES LYING IN A SURFACE OF E3 OR E31

2024-12-09T03:20:40+00:00

The differential equation characterizing a spherical curve in R3 expresses the radius of curvature of the curve in terms of its torsion. In this paper we show that the differential equation characterizing a curve lying in an oriented surface E3 or E31 allows two express the radius of the curvature of the curve in terms of its torsions. We give two examples for illustrate our main result.

Riemannian Maps From Kaehler Manifold With Generic Fibers

2024-12-09T03:23:10+00:00

We study Riemannian maps from almost Hermitian manifolds to Riemannian manifolds for the case when the fibers are generic submanifold of the total space. We obtain the integrability conditions for the distributions while vertical distribution is always integrable. We also study the geometry of the leaves of the distribution which arise from such maps, and obtain the necessary and sufficient conditions for the fibers as well as the total manifold to be generic product manifolds. We, further, obtain the necessary and sufficient condition for such maps to be totally geodesic.

Riemannian manifold admitting a new type of semi-symmetric non-metric connection

2024-12-09T03:23:46+00:00

We define a new type of semi-symmetric non-metric connection on a Riemannian manifold and established its existence. Further, we find some basic results of curvature tensor and Ricci tensor. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also studied some properties of submanifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection. To validate our findings, we construct two non-trivial examples of 3-dimensional and 5-dimensional Riemannian manifold equipped with a semi-symmetric non-metric connection.

On the Lanczos Potential

2024-12-09T03:24:15+00:00

For arbitrary geometries of Petrov types III, N and O we construct the Lanczos potential for the corresponding Weyl tensor. This will provide a technique to construct Lanczos potential in non-vacuum cases.

Does Vacuum Energy Allow for Computational “Bits” at the Start of Cosmological Evolution, and Their Possible Ties to Torsion Physics

2024-12-09T03:24:48+00:00

Based on the notion that torsion cancels cosmological vacuum energy [1], we
consider if relic black holes at the start of inflation may allow for the observed
cosmological constant. If thermal energy used at the start of inflation creates
conceptual issues, an energy term based on Corda’s treatment of black holes
may provide a solution, a leftover cosmological constant 10−121 times vacuum
energy. Considerations as to how black-hole physics may contribute to torsion
and the cosmological constant are considered in several numerical cases. Also
we present entanglement entropy in the early universe with a shrinking scale
factor [2] and show that consequences arise due to initial entangled for a timedependent
horizon radius in cosmology with flat space conditions for conformal
time. This construction preserves a minimum nonzero vacuum energy, and, in
doing so, keeps the computational bits for cosmological evolution. The bits are
ascribed to initial torsion as we describe.

Common fixed point theorems for C-class functions in b-metric spaces with application

2024-12-09T03:25:35+00:00

In this paper, we establish the existence and uniqueness of common fixed point theorems for self mappings satisfying the common limit range property with respect to mappings S and T and common (E.A)-property via the concept of C-class functions in b-metric spaces. We furnish two examples to validate our results. Our results improve various results appeared in the current literature. As an application, We provide the existence of a solution of an integral equations.

TILTED LRS BIANCHI TYPE-VIo DARK ENERGY COSMOLOGICAL MODEL

2024-12-09T03:26:07+00:00

Tilted LRS Bianchi-VIo dark energy cosmological model is investigated in Einstein’s theory of gravitation. We obtained solutions by considering shear scalar proportional to expansion scalar and deceleration parameter. Further we obtained an accelerating universe subject to the small value of the anisotropic parameter. Some physical and geometrical properties of the solutions are also discussed.