Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor

TL;DR

This paper introduces biconservative hypersurfaces with divergence-free stress-bienergy tensor and classifies such surfaces in 3D space forms, advancing understanding of their geometric properties.

Contribution

It defines biconservative hypersurfaces and provides a local classification of these surfaces in three-dimensional space forms, a novel contribution in differential geometry.

Findings

Classification of biconservative surfaces in 3D space forms

Introduction of the concept of hypersurfaces with divergence-free stress-bienergy tensor

New insights into the geometry of hypersurfaces with conserved stress-energy

Abstract

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.