Kodai Mathematical Journal

Linear Weingarten spacelike hypersurfaces in Lorentz space forms with prescribed Gauss map

Xiaoli Chao and Yusha Lv

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Abstract

This paper address the geometry of complete linear Weingarten spacelike hypersurfaces in the Lorentz space forms. First, a divergence lemma concerning linear Weingarten spacelike hypersurfaces is obtained. Then, with the aid of this lemma, by supposing suitable restrictions on the Gauss map, we show that such hypersurfaces must be totally umbilical, which are some extension of the recent results of Aquino, Bezerra and Lima [7] and Aquino, Lima and Velásquez [11].

Article information

Source
Kodai Math. J., Volume 41, Number 1 (2018), 98-114.

Dates
First available in Project Euclid: 19 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1521424826

Digital Object Identifier
doi:10.2996/kmj/1521424826

Mathematical Reviews number (MathSciNet)
MR3777389

Zentralblatt MATH identifier
06912403

Citation

Chao, Xiaoli; Lv, Yusha. Linear Weingarten spacelike hypersurfaces in Lorentz space forms with prescribed Gauss map. Kodai Math. J. 41 (2018), no. 1, 98--114. doi:10.2996/kmj/1521424826. https://projecteuclid.org/euclid.kmj/1521424826


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