On completeness of integral manifolds of nullity distributions

TL;DR

This paper provides a conceptual proof that maximal integral manifolds of the nullity distribution in complete submanifolds of space forms are themselves complete, focusing on points with minimal nullity index.

Contribution

It offers a new conceptual proof of the completeness of nullity distribution integral manifolds in space form submanifolds, extending understanding of their geometric properties.

Findings

Maximal integral manifolds of nullity distributions are complete in complete submanifolds of space forms.

The proof applies specifically to points with minimal nullity index.

The approach is conceptual, offering new insights into the geometry of submanifolds.

Abstract

We give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are complete.