Turkish Journal of Mathematics
DOI
10.3906/mat-1710-1
Abstract
$\xi$-Submanifolds in the Euclidean spaces are a natural extension of self-shrinkers and a generalization of $\lambda$-hypersurfaces. Moreover, $\xi$-submanifolds are expected to take the place of submanifolds with parallel mean curvature vector. In this paper, we establish a Bernstein-type theorem for $\xi$-submanifolds in the Euclidean spaces. More precisely, we prove that an $n$-dimensional smooth graphic $\xi$-submanifold with flat normal bundle in $\mathbb{R}^{n+p}$ is an affine $n$-plane.
Keywords
$\xi$-Submanifold, Bernstein-type theorem
First Page
36
Last Page
43
Recommended Citation
Jiang, Xu-Yong; SUN, HE-JUN; and ZHAO, PEIBIAO
(2019)
"A Bernstein-type theorem for $\xi$-submanifolds withflat normal bundle in the Euclidean spaces,"
Turkish Journal of Mathematics: Vol. 43:
No.
1, Article 4.
https://doi.org/10.3906/mat-1710-1
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss1/4
