In this work, we investigate the differential geometric characteristics of pedal and primitive curves in a Minkowski plane. A primitive is specified by the opposite structure for creating the pedal, and primitivoids are known as comparatives of the primitive of a plane curve. We inspect the relevance between primitivoids and pedals of plane curves that relate with symmetry properties. Furthermore, under the viewpoint of symmetry, we expand these notions to the frontal curves in the Minkowski plane. Then, we present the relationships and properties of the frontal curves in this category. Numerical examples are presented here in support of our main results.

Primitivoids of curves in Minkowski plane

The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of timelike circular surface was determined and named the timelike roller coaster surface. Meanwhile, we support the results of this work with some examples.

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Timelike Circular Surfaces and Singularities in Minkowski 3-Space

E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler–Savary, and Disteli’s formulae were derived.

/pdf/one-parameter-lorentzian-dual-spherical-movements-and-3i1ot2br.pdf

One-Parameter Lorentzian Dual Spherical Movements and Invariants of the Axodes

In the present note, we characterize Clairaut semi-invariant Riemannian maps from cosymplectic manifolds to Riemannian manifolds. Moreover, we provide a nontrivial example of such a Riemannian map.

/pdf/a-study-of-clairaut-semi-invariant-riemannian-maps-from-1m2oi6r1.pdf

A Study of Clairaut Semi-Invariant Riemannian Maps from Cosymplectic Manifolds

The present research paper consists of the study of an η1-Einstein soliton in general relativistic space-time with a torse-forming potential vector field. Besides this, we try to evaluate the characterization of the metrics when the space-time with a semi-symmetric energy-momentum tensor admits an η1-Einstein soliton, whose potential vector field is torse-forming. In adition, certain curvature conditions on the space-time that admit an η1-Einstein soliton are explored and build up the importance of the Laplace equation on the space-time in terms of η1-Einstein soliton. Lastly, we have given some physical accomplishment with the connection of dust fluid, dark fluid and radiation era in general relativistic space-time admitting an η1-Einstein soliton.

/pdf/general-relativistic-space-time-with-e1-einstein-metrics-1e672zis.pdf

General Relativistic Space-Time with η1-Einstein Metrics

In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.

/pdf/improved-chen-s-inequalities-for-submanifolds-of-generalized-2iz3ztwu.pdf

Improved Chen's Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

In this paper, we studied the geometrical aspects of a perfect fluid spacetime with torse-forming vector field $$\xi $$
 under certain curvature restrictions, and Ricci–Yamabe soliton and $$\eta $$
 -Ricci–Yamabe soliton in a perfect fluid spacetime. Conditions for the Ricci–Yamabe soliton to be steady, expanding or shrinking are also given. Moreover, when the potential vector field $$\xi $$
 of $$\eta $$
 -Ricci–Yamabe soliton is of gradient type, we derive a Poisson equation and also looked at its particular cases. Lastly, a non-trivial example of perfect fluid spacetime admitting $$\eta $$
 -Ricci–Yamabe soliton is constructed.

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

Abstract The purpose of the present paper is to examine the isometries of almost Ricci–Yamabe solitons. Firstly, the conditions under which a compact gradient almost Ricci–Yamabe soliton is isometric to Euclidean sphere $$S^n(r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are obtained. Moreover, we have shown that the potential f of a compact gradient almost Ricci–Yamabe soliton agrees with the Hodge–de Rham potential h . Next, we studied complete gradient almost Ricci–Yamabe soliton with $$\alpha \ne 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and non-trivial conformal vector field with non-negative scalar curvature and proved that it is either isometric to Euclidean space $$E^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> or Euclidean sphere $$S^n.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Also, solenoidal and torse-forming vector fields are considered. Lastly, some non-trivial examples are constructed to verify the obtained results. 

/pdf/isometries-on-almost-ricci-yamabe-solitons-6mfwhw0i.pdf

Isometries on almost Ricci–Yamabe solitons

The goal of this paper is the introduction of hyper generalized φ-recurrent (k, μ)-contact metric manifolds and of quasi generalized φrecurrent (k, μ)-contact metric manifolds, and the investigation of their properties. Their existence is guaranteed by examples.

http://www.koreascience.or.kr:80/article/JAKO202031064817205.pdf

On a class of generalized recurrent $(k,\mu)$-contact metric manifolds

. The object of the present paper is to investigate some geometric and physical properties of weakly cyclic B symmetric ( WCBS ) 4 spacetime under certain conditions. At first, the existence of ( WCBS ) 4 spacetime is showed by constructing a non-trivial example. Then it is shown that a ( WCBS ) 4 spacetime with harmonic Weyl tensor is a Yang Pure space or the integral curve of vector field ρ are geodesic and vector field ρ is irrotational, provided r = ba . Moreover some geometric properties of ( WCBS ) 4 spacetime satisfying certain curvature restrictions are investigated and shown that conformally flat ( WCBS ) 4 spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field ρ . Next we characterize viscous fluid, dust and perfect fluid ( WCBS ) 4 spacetimes and obtained interesting results. Finally, we showed that in a ( WCBS ) 4 spacetime with non-constant scalar curvature satisfying divC = 0 and fulfilling the condition r = ba , if ρ is Killing vector then it is Weyl compatible, purely electric spacetime and its possible Petrov types are I or D. M.S.C. 2010 : 53B30,

Mohan Khatri

Papers

Improved Chen's Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

Isometries on almost Ricci–Yamabe solitons

On a class of generalized recurrent $(k,\mu)$-contact metric manifolds

On weakly cyclic B symmetric spacetime