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HOME > Table of Contents and Abstracts > Vol. 77, No. 1
Tohoku Mathematical Journal
2025
March
SECOND SERIES VOL. 77, NO. 1
Tohoku Math. J.
77 (2025), 105-118
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Title
RIGIDITY RESULTS OF SPACE-LIKE SUBMANIFOLDS WITH PARALLEL GAUSSIAN MEAN CURVATURE VECTOR
Author
Huijuan Wang
(Received January 17, 2023) |
Abstract.
In this paper, we study the space-like submanifolds with parallel Gaussian mean curvature vector in pseudo-Euclidean space. We establish a relevant Omori-Yau maximum principle for these space-like submanifolds which is closed with respect to the Euclidean topology. Then, we prove a rigidity theorem for these space-like submanifolds with $\|\xi\| < \sqrt{\frac2n}$ under a growth condition on the mean curvature. Finally, we use a Liouville type result to obtain a further rigidity theorem for space-like submanifolds with parallel Gaussian mean curvature vector in pseudo-Euclidean space.
Mathematics Subject Classification.
Primary 53C40; Secondary 53C24.
Key words and phrases.
Rigidity theorems, space-like submanifolds, parallel Gaussian mean curvature vector, Omori-Yau maximum principle.
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