[1] Wang Peijun, Chao Xiaoli, Bai Miaomiao,. Linear Weingarten spacelike hypersurfacein locally symmetric Lorentz space [J]. Journal of Southeast University (English Edition), 2018, 34 (2): 276-280. [doi:10.3969/j.issn.1003-7985.2018.02.018]

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Linear Weingarten spacelike hypersurfacein locally symmetric Lorentz space()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

34

Issue:

2018 2

Page:

276-280

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2018-06-20

Info

Title:

Linear Weingarten spacelike hypersurfacein locally symmetric Lorentz space

Author(s):

Wang Peijun;  Chao Xiaoli;  Bai Miaomiao

School of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

spacelike hypersurface;  linear Weingarten;  locally symmetric Lorentz space

PACS:

O186.1

DOI:

10.3969/j.issn.1003-7985.2018.02.018

Abstract:

The rigidity of spacelike hypersurface Mⁿ immersed in locally symmetric space Mⁿ⁺¹₁ is investigated, where the(normalized)scalar curvature R and mean curvature H of Mⁿ satisfy R=aH+b, and a, b are real constants. First, an estimate of the upper bound of the function L(nH)is given, where L is a second-order differential operator. Then, under the assumption that the square norm of the second fundamental form is bounded by a given positive constant, it is proved that Mⁿ must be either totally umbilical or contain two distinct principle curvatures, one of which is simple. Moreover, a similar result is obtained for complete noncompact spacelike hypersurfaces in locally symmetric Einstein spacetime. Hence, some known rigidity results for hypersurface with constant scalar curvature are extended for the linear Weingarten case.

References:

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Memo

Memo:

Biographies: Wang Peijun(1989—), male, Ph.D.candidate; Chao Xiaoli(corresponding author), male, doctor, professor, xlchao@seu.edu.cn.
Foundation items: The Natural Science Foundation of Jiangsu Province(No.BK20161412), the Fundamental Research Funds for the Central Universities, the Scientific Innovation Research of College Graduates in Jiangsu Province(No. KYCX17_0041).
Citation: Wang Peijun, Chao Xiaoli, Bai Miaomiao. Linear Weingartenspacelike hypersurface in locally symmetric Lorentz space[J].Journal of Southeast University(English Edition), 2018, 34(2):276-280.DOI:10.3969/j.issn.1003-7985.2018.02.018.

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