Tohoku Mathematical Journal
2025

March
SECOND SERIES VOL. 77, NO. 1

Tohoku Math. J.
77 (2025), 105-118

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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