2024 : 11 : 23
Firooz Pashaie

Firooz Pashaie

Academic rank: Associate Professor
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Education: PhD.
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Research

Title
On bi-conservative hypersurfaces in the Lorentz-Minkowski 4-space E_1^4 4 1
Type
JournalPaper
Keywords
Lorentz hypersurface, bi-conservative, bi-harmonic, isoparametric.
Year
2023
Journal Sahand Communications in Mathematical Analysis
DOI
Researchers Firooz Pashaie

Abstract

In the 1920s, D. Hilbert has showed that the tensor of stress-energy, related to a given functional $\Lambda$, is a conservative symmetric bicovariant tensor $\Theta$ at the critical points of $\Lambda$, which means that div$\Theta =0$. As a routine extension, the bi-conservative condition (i.e. div$\Theta_2=0$) on the tensor of stress-bienergy $\Theta_2$ is introduced by G. Y. Jiang (in 1987). This subject has been followed by many mathematicians. In this paper, we study an extended version of bi-conservativity condition on the Lorentz hypersurfaces of the Einstein space. A Lorentz hypersurface $M_1^3$ isometrically immersed into the Einstein space is called $\mathcal{C}$-bi-conservative if it satisfies the condition $\n_2(\nabla H_2)=\frac{9}{2} H_2\nabla H_2$, where $\n_2$ is the second Newton transformation, $H_2$ is the 2nd mean curvature function on $M_1^3$ and $\nabla$ is the gradient tensor. We show that the $\C$-bi-conservative Lorentz hypersurfaces of Einstein space have constant second mean curvature.