On submanifolds with recurrent second fundamental form in spaces of constant curvature

TL;DR

This paper classifies and describes n-dimensional submanifolds with recurrent, nonparallel second fundamental form in spaces of constant curvature, advancing understanding of their geometric properties.

Contribution

It provides the complete local classification and geometric description of such submanifolds, a novel result in differential geometry.

Findings

Classification of submanifolds with recurrent second fundamental form

Geometric descriptions of these submanifolds

Extension of known results in spaces of constant curvature

Abstract

The complete local classification and geometric description of n-dimensional submanifolds F with recurrent nonparallel second fundamental form in the spaces of constant curvature M(c) are obtained in this article.