On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space

Abstract

In this paper, we mainly investigate (contra)pedals and (anti)orthotomics of frontals in the de Sitter 2-space from the viewpoint of singularity theory and differential geometry. We utilize the de Sitter Legendrian Frenet frames to provide parametric representations of (contra)pedal curves of spacelike and timelike frontals in the de Sitter 2-space and to investigate the geometric and singularity properties of these (contra)pedal curves. We then introduce orthotomics of frontals in the de Sitter 2-space and explain these orthotomics as wavefronts from the viewpoint of Legendrian singularity theory. Furthermore, we generalize these methods to study antiorthotomics of frontals in the de Sitter 2-space.

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

“…The methods described in this paper can be used for other classes of submanifolds in various ambient spaces endowed with a semi-symmetric metric connection. For example, we can combine the methods in this paper with the technics and results in [30][31][32][33][34][35][36][37][38] to obtain more interesting results relate with symmetry. In order to study corresponding problems for submanifolds in space forms endowed with a semi-symmetric non-metric connection, it is necessary to define a suitable sectional curvature.…”

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

“…From (34), the system of differential equations for the slant curve C in M is dx ds (s) = 1 + a 2 sinγe −z , dy ds (s) = 1 + a 2 (sinγ + cosγ)e −z , dz ds (s) = aα.…”

“…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.…”

Estimation of Ricci Curvature for Hemi-Slant Warped Product Submanifolds of Generalized Complex Space Forms and Their Applications

“…θ be a hemi-slant wp submanifold of a g. c. s. f. Through the Gauss equation, we find (28) as below.…”

“…The characterization of differential equations on Riemannian manifolds has grown to be an exciting area of study and has been looked into by many scholars, including these in [24][25][26]. Furthermore, we will combine the methods and results in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] for future research to obtain more new developments. Note: Throughout the paper, we used the abbreviations w p for "warped product", g.c.s.f for "generalized complex space form", TG for "totally geodesic", and TU for "totally umbilical".…”