On the Gauss Map with Vanishing Biharmonic stress-energy tensor

TL;DR

This paper investigates the conditions under which the Gauss map's biharmonic stress-energy tensor vanishes, showing that under certain assumptions, it implies the map is harmonic, thus linking biharmonic and harmonic properties.

Contribution

It establishes a connection between vanishing biharmonic stress-energy tensor and harmonicity of the Gauss map under specific assumptions.

Findings

Vanishing $S_2$ implies harmonicity under certain conditions.

Provides new insights into the geometric properties of Gauss maps.

Enhances understanding of biharmonic stress-energy tensors in differential geometry.

Abstract

We study the biharmonic stress-energy tensor $S_2$ of Gauss map. Adding few assumptions, the Gauss map with vanishing $S_2$ would be harmonic.