A Bernstein-type theorem for $\xi$-submanifolds with flat normal bundle in the Euclidean spaces

Authors : Xu-yong JİANG, He-jun SUN, PEIBIAO ZHAO

Pages : 36-43

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Publication Date : 0000-00-00

Article Type : Research Paper

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