@article {
author = {Pashaie, Firooz},
title = {On bi-conservative hypersurfaces in the Lorentz-Minkowski 4-space $E_1^4$},
journal = {Sahand Communications in Mathematical Analysis},
volume = {},
number = {},
pages = {-},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.1982815.1215},
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.},
keywords = {Lorentz hypersurface,bi-conservative,bi-harmonic,isoparametric},
url = {https://scma.maragheh.ac.ir/article_703150.html},
eprint = {}
}