Biharmonic Hypersurfaces With The Recurrent Operators In The Euclidean Space

TL;DR

This paper explores the role of recurrent operators like curvature, Ricci, Jacobi, shape, and Weyl in determining when biharmonic hypersurfaces in Euclidean space are minimal, highlighting their significance in geometric analysis.

Contribution

It demonstrates the influence of various recurrent operators on biharmonic hypersurfaces, establishing conditions for minimality in Euclidean space.

Findings

Recurrent curvature operator impacts minimality of biharmonic hypersurfaces.

Recurrent Ricci and Jacobi operators are significant in hypersurface minimality.

Recurrent shape and Weyl operators play a crucial role in the geometry of biharmonic hypersurfaces.

Abstract

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.