arXiv subjects

Esmaiel Abedi

Publications and source records attributed to Esmaiel Abedi.

6 recordsLinked to original sources

arXiv2021

The Variational Geometry of Surfaces in the Conformally Flat Space

In this paper, close surfaces are considered in 3-dimensional harmonic conformally flat space in point of the variation. It is shown that if the conformal vector field be tangent to surface and the sign of the mean curvature does not change then surface is minimal. Also, it is determined that the critical point of mean curvature functional is homeomorphic to the sphere. Furthermore, the Euler-Lagrange equations associated to the mean curvature and Willmore functionals are determined.

math.DG↗

arXiv2021

Biharmonic Hypersurfaces With The Recurrent Operators In The Euclidean Space

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

math.DG↗

arXiv2021

Survey on the Biharmonic Hypersurfaces in Terms of the Induced Metric of Tensor Ricci

In this article, we study the biharmonic hypersurfaces in the Sasakian space form with the induced metric of tensor Ricci. We find the existence necessary and sufficient condition of the biharmonic hypersurfaces there. We show that the biharmonic Hopf hypersurfaces are minimal where gradient of the mean curvature is in direction of the structural vector fields. Furthermore, we prove that does not exist any biharmonic Hopf hypersurfaces when the gradient of the mean curvature is a principal direction.

math.DG↗

arXiv2021

Biharmonic CMC Hypersurfaces in the Warped Product Space

We find the necessary and sufficient condition for the proper biharmonic CMC hypersurfaces in the special warped product space. Furthermore, we obtain that there exists no proper biharmonic CMC compact hypersurface there.

math.DG↗

arXiv2021

Tanaka-Webster biharmonic hypersurfaces in the Sasakian space form

In this article we consider the concept of biharmonicity about the hypersurfaces in the Sasakian space form which is equipped with the Tanaka-Webster connection.

math.DG↗

arXiv2016

Special solitons on 3-manifolds

In this paper, we study solitons on $3$-dimensional manifolds. In particular, we show that $3$-dimensional pseudo-symmetric gradient Ricci solitons and nontrivial gradient Yamabe solitons are locally isometric to either $\mathbb{R}^{3}$, $\mathbb{S}^{3}$, $\mathbb{H}^{3}$, $\mathbb{R} \times \mathbb{S}^{2}$ or $\mathbb{R} \times \mathbb{H}^{2}$.

math.DG↗