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arXiv · 1607.08649

Complete minimal submanifolds with nullity in Euclidean space

M. Dajczer·Th. Kasioumis·A. Savas-Halilaj·Th. Vlachos
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Abstract

In this paper, we investigate minimal submanifolds in Euclidean space with positive index of relative nullity. Let $M^m$ be a complete Riemannian manifold and let $f\colon M^m\to\R^n$ be a minimal isometric immersion with index of relative nullity at least $m-2$ at any point. We show that if the Omori-Yau maximum principle for the Laplacian holds on $M^m$, for instance, if the scalar curvature of $M^m$ does not decrease to $-\infty$ too fast or if the immersion $f$ is proper, then the submanifold must be a cylinder over a minimal surface.

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BibTeXRIS

M. Dajczer, Th. Kasioumis, A. Savas-Halilaj, Th. Vlachos. 2016-07-28. Complete minimal submanifolds with nullity in Euclidean space. https://arxiv.org/abs/1607.08649

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