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

118124

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

Öz $\xi$-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.

Anahtar Kelimeler:

$\xi$-Submanifold, Bernstein-type theorem

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

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