Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces

Section: Discussionmentioning

confidence: 99%

Optimal Inequalities for Submanifolds in Trans-Sasakian Manifolds Endowed with a Semi-Symmetric Metric Connection

Iordache

Mohammed

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.

“…Moreover, the pursuit of interdisciplinary research holds great promise for producing valuable insights. In forthcoming research, we intend to explore additional applications of the primary findings presented in this paper to soliton theory, submanifold theory, and related areas, as examined in [1,2,21,[44][45][46][47][48][49][50][51][52][53][54][55][56], with the goal of achieving new results.…”

Section: Discussionmentioning

confidence: 99%

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

Hakami,

Siddiqi

2023

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.