On the curvatures of timelike circular surfaces in Lorentz-Minkowski space

Filomat, Год журнала: 2024, Номер 38(4), С. 1423 - 1437

Опубликована: Янв. 1, 2024

In this paper, using the classical methods of differential geometry, wedefine invariants timelike circular surfaces in Lorentz-Minkowski space R3 1, called curvature functions, and show kinematic meaning these invariants. Then we discuss properties give a kind classification with theories Besides, to demonstrate our theoretical results some computational examples are given plotted.

Язык: Английский

---

Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection

AIMS Mathematics, Год журнала: 2023, Номер 8(8), С. 17335 - 17353

Опубликована: Янв. 1, 2023

<abstract><p>Let $ (M, g) be an n $-dimensional (pseudo-)Riemannian manifold and TM its tangent bundle equipped with the complete lift metric ^{C}g $. First, we define a Ricci quarter-symmetric connection \overline{\nabla } on Second, compute all forms of curvature tensors study their properties. We also mean gradient solitons are important topics studied extensively lately. Necessary sufficient conditions for to become soliton concerning presented. Finally, search locally conformally flat respect $.</p></abstract>

Язык: Английский

---

On simultaneous characterizations of partner-ruled surfaces in Minkowski 3-space

AIMS Mathematics, Год журнала: 2023, Номер 8(9), С. 22256 - 22273

Опубликована: Янв. 1, 2023

<abstract><p>In this study, the partner-ruled surfaces in Minkowski 3-space, which are defined according to Frenet vectors of non-null space curves, introduced with extra conditions that guarantee existence definite surface normals. First, requirements each pair be simultaneously developable and minimal (or maximal for spacelike surfaces) investigated. The also characterize asymptotic, geodesic curvature lines parameter curves these surfaces. Finally, study provides examples timelike includes their graphs.</p></abstract>

Язык: Английский

---

On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space

Mathematics, Год журнала: 2023, Номер 11(15), С. 3365 - 3365

Опубликована: Авг. 1, 2023

The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived expression for the homogeneous generalized Matsumoto change. Moreover, deduced aforementioned space vanishing S-curvature. These findings contribute significantly to understanding complex nature their properties.

Язык: Английский

---

A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space E25

Mathematics, Год журнала: 2023, Номер 11(15), С. 3427 - 3427

Опубликована: Авг. 7, 2023

We present a family of hypersurfaces revolution distinguished by four parameters in the five-dimensional pseudo-Euclidean space E25. The matrices corresponding to fundamental form, Gauss map, and shape operator this are computed. By utilizing Cayley–Hamilton theorem, we determine curvatures specific family. Furthermore, establish criteria for maximality within framework. Additionally, reveal relationship between Laplace–Beltrami 5×5 matrix.

Язык: Английский

---

Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces

Axioms, Год журнала: 2023, Номер 12(5), С. 486 - 486

Опубликована: Май 17, 2023

In this article, we examine the relationship between Darboux frames along parameter curves and frame of base curve ruled surface. We derive equations quaternionic shape operators, which can rotate tangent vectors around normal vector, find corresponding rotation matrices. Using these Gauss curvature mean explore how properties are found by use Frenet instead generator vectors. provide illustrative examples to better demonstrate concepts results discussed.

Язык: Английский

---

Kinematic-geometry of a line trajectory and the invariants of the axodes

Demonstratio Mathematica, Год журнала: 2023, Номер 56(1)

Опубликована: Янв. 1, 2023

Abstract In this article, we investigate the relationships between instantaneous invariants of a one-parameter spatial movement and local axodes. Specifically, provide new proofs for Euler-Savary Disteli formulas using E. Study map in kinematics, showcasing its elegance efficiency. addition, introduce two line congruences thoroughly analyze their equivalence. Our findings contribute to deeper understanding interplay movements axodes, with potential applications fields such as robotics mechanical engineering.

Язык: Английский

---

Geometric classifications of k-almost Ricci solitons admitting paracontact metrices

Open Mathematics, Год журнала: 2023, Номер 21(1)

Опубликована: Янв. 1, 2023

Abstract The prime objective of the approach is to give geometric classifications k k -almost Ricci solitons associated with paracontact manifolds. Let M 2 n + 1 ( φ , ξ η g ) {M}^{2n+1}\left(\varphi ,\xi ,\eta ,g) be a metric manifold, and if K K -paracontact g represents soliton V λ \left(g,V,k,\lambda ) potential vector field V Jacobi along Reeb \xi , then either = − k=\lambda -2n or -Ricci soliton. Next, we consider manifold as infinitesimal transformation collinear . We have proved that non-zero operator Q Q commutes structure \varphi it Einstein constant scalar curvature equals -2n\left(2n+1) Finally, deduced para-Sasakian admitting gradient

Язык: Английский

---

Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection

Symmetry, Год журнала: 2023, Номер 15(8), С. 1553 - 1553

Опубликована: Авг. 8, 2023

The purpose of this study is to examine the complete lifts from symmetric and concircular n-dimensional Lorentzian para-Sasakian manifolds (briefly, (LPS)n) its tangent bundle TM associated with a Riemannian connection DC quarter-symmetric metric (QSMC) D¯C.

Язык: Английский

---

Characterization of Ricci Almost Soliton on Lorentzian Manifolds

Symmetry, Год журнала: 2023, Номер 15(6), С. 1175 - 1175

Опубликована: Май 31, 2023

Ricci solitons (RS) have an extensive background in modern physics and are extensively used cosmology general relativity. The focus of this work is to investigate almost (RAS) on Lorentzian manifolds with a special metric connection called semi-symmetric u-connection (SSM-connection). First, we show that any quasi-Einstein manifold having SSM-connection, whose RS, Einstein manifold. A similar conclusion also holds for SSM-connection admitting RS soliton vector Z parallel the u. Finally, examine gradient (GRAS) SSM-connection.

Язык: Английский

---