Kenmotsu Metric as Conformal $$\eta $$-Ricci Soliton

In this manifestation, we explain the geometrisation of η-Ricci–Yamabe soliton and gradient η-Ricci–Yamabe soliton on Riemannian submersions with the canonical variation. Also, we prove any fiber of the same submersion with the canonical variation (in short CV) is an η-Ricci–Yamabe soliton, which is called the solitonic fiber. Also, under the same setting, we inspect the η-Ricci–Yamabe soliton in Riemannian submersions with a φ(Q)-vector field. Moreover, we provide an example of Riemannian submersions, which illustrates our findings. Finally, we explore some applications of Riemannian submersion along with cohomology, Betti number, and Pontryagin classes in number theory.

Section: Discussionmentioning

confidence: 99%

Significance of Solitonic Fibers in Riemannian Submersions and Some Number Theoretic Applications

Hakami,

Siddiqi

2023

“…As a future work, we plan to proceed to study some applications of contact magnetic curves and slant curves with singularity theory and submanifold theory, etc. in [34][35][36][37] to obtain new results and theorems.…”

Section: Discussionmentioning

confidence: 99%

Two Special Types of Curves in Lorentzian α-Sasakian 3-Manifolds

Chen

Liu

2023

In this paper, we focus on the research and analysis of the geometric properties and symmetry of slant curves and contact magnetic curves in Lorentzian α-Sasakian 3-manifolds. To do this, we define the notion of Lorentzian cross product. From the perspectives of the Legendre and non-geodesic curves, we found the ratio relationship between the curvature and torsion of the slant curve and contact magnetic curve in the Lorentzian α-Sasakian 3-manifolds. Moreover, we utilized the property of the contact magnetic curve to characterize the manifold as Lorentzian α-Sasakian and to find the slant curve type of the Frenet contact magnetic curve. Furthermore, we found an example to verify the geometric properties of the slant curve and contact magnetic curve in the Lorentzian α-Sasakian 3-manifolds.

“…Hopefully, these scores will be useful in the field of differential geometry and to physicists and others exploring general relativity theory. Our future research will investigate how the principal findings presented in this study can be applied to generate fresh outcomes in conjunction with soliton theory, submanifold theory, and other pertinent fields that have been discussed in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”

Section: Discussionmentioning

confidence: 99%

A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space

Nazra,

Abdel-Baky

2023

The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process.