Biharmonic orbits of isotropy representations of symmetric spaces

TL;DR

This paper characterizes when orbits of isotropy representations of symmetric spaces are biharmonic in hyperspheres, providing new examples of higher co-dimension biharmonic submanifolds.

Contribution

It establishes a necessary and sufficient condition for such orbits to be biharmonic, expanding the class of known biharmonic submanifolds in hyperspheres.

Findings

Derived a criterion for biharmonicity of isotropy orbits

Constructed examples of higher co-dimension biharmonic submanifolds

Enhanced understanding of biharmonic submanifolds in symmetric spaces

Abstract

In this paper, we give a necessarly and sufficient condition for orbits of linear isotropy representations of Riemannian symmetric spaces are biharmonic submanifolds in hyperspheres in Euclidean spaces. In particular, we obtain examples of biharmonic submanifolds in hyperspheres whose co-dimension is greater than one.