Abstract
We deal with $n$-dimensional complete submanifolds immersed with parallel nonzero mean curvature vector ${\bf H}$ in the hyperbolic space $\mathbb{H}^{n+p}$. In this setting, we establish sufficient conditions to guarantee that such a submanifold $M^n$ must be pseudo-umbilical, which means that ${\bf H}$ is an umbilical direction. In particular, we conclude that $M^n$ is a minimal submanifold of a small hypersphere of $\mathbb{H}^{n+p}$.
Citation
Henrique F. de Lima. Fábio R. dos Santos. Marco Antonio L. Velásquez. "On the geometry of complete submanifolds immersed in the hyperbolic space." Bull. Belg. Math. Soc. Simon Stevin 22 (5) 707 - 713, december 2015. https://doi.org/10.36045/bbms/1450389242
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