arXiv subjects

Akhilesh Yadav

Publications and source records attributed to Akhilesh Yadav.

9 recordsLinked to original sources

arXiv2026

Design, Fabrication and Testing of a D-Shaped High Temperature Superconducting Magnet

High-temperature technical superconductors are potential candidates for compact and high-field tokamak magnets. The demand for higher fusion power can be met with an on-axis high magnetic field due to toroidal magnets. An R&D activity has been initiated at the Institute for Plasma Research, India, to develop a compact D-shaped superconducting magnet utilizing REBCO high-temperature superconducting tapes. Under this initiative, a toroidal configuration with a major radius of 0.42 m, consisting of eight D-shaped, four poloidal field, and a central solenoid high-temperature superconducting magnets producing an on-axis toroidal magnetic field of 0.23 T has been conceptualized. The fabrication feasibility of a D-shaped coil for this toroidal configuration also envisaged using stacked high-temperature superconducting cable. In this paper, we report the design of a compact D-shaped coil, the fabrication of a long length HTS cable, a winding pack, and its integration with a cryogenic casing and vacuum enclosure. The winding pack terminations, joints, its interfacing with the power supply, and performance testing are also reported in this paper.

physics.acc-ph↗

arXiv2025

Almost Gradient Ricci Solitons on Static Spacetime

The aim of this paper is to study geometrical aspects of static spacetime admitting an almost gradient Ricci soliton. Among others, We first determine the conditions under which the base manifold of static spacetime possess an almost gradient Ricci soliton and we show that the almost gradient Ricci soliton become steady gradient Ricci soliton when static spacetime turns to a vacuum static spacetime. Next, we exhibit that an expanding almost gradient Ricci soliton on base manifold of non-compact and connected static spacetime satisfies shr$\ddot{o}$dinger's equation for a smooth function $f$. Also, we find the soliton constant under which the static perfect fluid spacetime with almost gradient Ricci soliton holds the null convergence condition and the strong energy condition. Further, we study the almost gradient Ricci soliton on base manifold of static perfect fluid spacetime with potential function as warping function and it is shown that the base manifold of a static perfect fluid spacetime with an almost gradient Ricci soliton is an Einstein manifold. Next, we obtain a necessary and sufficient condition on soliton constant to obey timelike convergence condition. Further, we obtain some results for Ricci symmetric and weakly Ricci symmetric base manifold of static perfect fluid spacetime admitting gradient Ricci soliton. Finally, we find the nature of almost gradient Ricci soliton on $4$-dimensional half conformally flat base manifold of static perfect fluid spacetime.

math.DG↗

arXiv2023

Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton

In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds with non-trivial examples. First, we study some properties of the O'Neill tensor $A$ in the case of conformal submersion. We also find a necessary and sufficient condition for conformal submersion to be totally geodesic and calculate the Ricci tensor for the total manifold of such a map with different assumptions. Further, we consider a conformal submersion $F:M \to N$ from a Ricci soliton to a Riemannian manifold and obtain necessary conditions for the fibers of $F$ and the base manifold $N$ to be Ricci soliton, almost Ricci soliton and Einstein. Moreover, we find necessary conditions for a vector field and its horizontal lift to be conformal on $N$ and $(KerF_\ast)^\bot,$ respectively. Also, we calculate the scalar curvature of Ricci soliton $M$. Finally, we obtain a necessary and sufficient condition for $F$ to be harmonic.

math.DG↗

arXiv2023

Riemannian maps whose base manifolds admit a Ricci soliton

In this paper, we study Riemannian maps whose base manifolds admit a Ricci soliton and give a non-trivial example of such a Riemannian map. First, we find Riemannian curvature tensor for the base manifolds of Riemannian map $F$. Further, we obtain the Ricci tensor and calculate the scalar curvature of the base manifold. Moreover, we obtain necessary conditions for the leaves of $rangeF_\ast$ to be Ricci soliton, almost Ricci soliton, and Einstein. We also obtain necessary conditions for the leaves of $(rangeF_\ast)^\bot$ to be Ricci soliton and Einstein. Also, we calculate the scalar curvatures of $rangeF_\ast$ and $(rangeF_\ast)^\bot$ by using Ricci soliton. Finally, we study the harmonicity and biharmonicity of such a Riemannian map. We obtain a necessary and sufficient condition for such a Riemannian map between Riemannian manifolds to be harmonic. We also obtain necessary and sufficient conditions for a Riemannian map from a Riemannian manifold to a space form that admits Ricci soliton to be harmonic and biharmonic.

math.DG↗

arXiv2023

Clairaut Riemannian maps

In this paper, first we define Clairaut Riemannian map between Riemannian manifolds by using a geodesic curve on the base space and find necessary and sufficient conditions for a Riemannian map to be Clairaut with a non-trivial example. We also obtain necessary and sufficient condition for a Clairaut Riemannian map to be harmonic. Thereafter, we study Clairaut Riemannian map from Riemannian manifold to Ricci soliton with a non-trivial example. We obtain scalar curvatures of $rangeF_\ast$ and $(rangeF_\ast)^\bot$ by using Ricci soliton. Further, we obtain necessary conditions for the leaves of $rangeF_\ast$ to be almost Ricci soliton and Einstein. We also obtain necessary condition for the vector field $\dotβ$ to be conformal on $rangeF_\ast$ and necessary and sufficient condition for the vector field $\dotβ$ to be Killing on $(rangeF_\ast)^\bot$, where $β$ is a geodesic curve on the base space of Clairaut Riemannian map. Also, we obtain necessary condition for the mean curvature vector field of $rangeF_\ast$ to be constant. Finally, we introduce Clairaut anti-invariant Riemannian map from Riemannian manifold to Kähler manifold, and obtain necessary and sufficient condition for an anti-invariant Riemannian map to be Clairaut with a non-trivial example. Further, we find necessary condition for $rangeF_\ast$ to be minimal and totally geodesic. We also obtain necessary and sufficient condition for Clairaut anti-invariant Riemannian maps to be harmonic.

math.DG↗

arXiv2022

Relatively normal-slant helices in Minkowski $3$-space

In this paper, we study relatively normal-slant helices lying on timelike as well as spacelike surfaces in Minkowski $3$-space $ \mathbb{E}_1^3$. The axes of spacelike and timelike relatively normal-slant helices are obtained via their Darboux frames. We also establish characterization theorems for spacelike and timelike relatively normal-slant helices in Minkowski $3$-space $\mathbb{E}_1^3$. Finally, the relationship between relatively normal-slant helices and slant helices is found on timelike as well as spacelike surfaces.

math.GM↗

arXiv2021

On Relatively Normal-Slant Helices and Isophotic Curves

In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an isophotic curve on a given surface by its parametric or implicit equation.

math.GM↗

arXiv2021

Some characterizations of rectifying curves on a smooth surface in Euclidean 3-space

In this paper, we investigate sufficient condition for the invariance of a rectifying curve on a smooth surface immersed in Euclidean 3-space under isometry by using Darboux frame $\left\lbrace T, P, U\right\rbrace$. Further, we find the deviations of the position vector of a rectifying curve on the smooth surface along any tangent vector $T = aϕ_u + bϕ_v$ with respect to the isometry. We also find the deviations of the position vector of a rectifying curve on the smooth surface along the unit normal $U$ to the surface and along $P (= U \times T)$ with respect to the isometry.

math.DG↗

arXiv2021

Darboux Rectifying curves on a smooth surface

The main aim of this paper is to investigate Darboux rectifying curves on a smooth surface immersed in the Euclidean space. First, we discuss the component of the position vector of a Darboux rectifying curve on a smooth immersed surface under the isometry of surfaces. Next we find a sufficient condition for the conformal invariance of Darboux rectifying curve.

math.DG↗