Cylindricity of complete Euclidean submanifolds with relative nullity

TL;DR

This paper extends the classical Hartman cylindricity theorem by showing that complete Euclidean submanifolds with positive minimal relative nullity index and controlled Ricci curvature decay are cylindrical.

Contribution

It generalizes the Hartman cylindricity theorem to submanifolds with specific Ricci curvature decay conditions.

Findings

Submanifolds with positive relative nullity are cylindrical under curvature decay.

The result applies to complete Euclidean submanifolds with minimal nullity index.

The theorem broadens understanding of submanifold geometry with curvature constraints.

Abstract

We show that a complete Euclidean submanifold with minimal index of relative nullity $\nu_0>0$ and Ricci curvature with a certain controlled decay must be a $\nu_0$-cylinder. This is an extension of the classical Hartman cylindricity theorem.