On bi-conservative hypersurfaces in the Lorentz-Minkowski ۴-space E_۱^۴
سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 102
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شناسه ملی سند علمی:
JR_SCMA-20-3_001
تاریخ نمایه سازی: 20 فروردین 1402
چکیده مقاله:
In the ۱۹۲۰s, 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 =۰. As a routine extension, the bi-conservative condition (i.e. div\Theta_۲=۰) on the tensor of stress-bienergy \Theta_۲ is introduced by G. Y. Jiang (in ۱۹۸۷). 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_۱^۳ isometrically immersed into the Einstein space is called \mathcal{C}-bi-conservative if it satisfies the condition n_۲(\nabla H_۲)=\frac{۹}{۲} H_۲\nabla H_۲, where n_۲ is the second Newton transformation, H_۲ is the ۲nd mean curvature function on M_۱^۳ and \nabla is the gradient tensor. We show that the C-bi-conservative Lorentz hypersurfaces of Einstein space have constant second mean curvature.
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نویسندگان
Firooz Pashaie
Department of Mathematics, Faculty of Science, University of Maragheh, P.O.Box ۵۵۱۸۱-۸۳۱۱۱, Maragheh, Iran.