Construction of $r$-harmonic submanifolds
Differential Geometry
2024-08-06 v2
Abstract
We provide a construction method for biharmonic submanifolds in cohomogeneity one manifolds. In particular, we give new examples of biharmonic submanifolds and study the normal index of these submanifolds. We use this strategy to construct metrics on the sphere admitting biharmonic non-minimal hypersurfaces with three distinct principal curvatures. Finally, we perform a similar study of -harmonic submanifolds of cohomogeneity one manifolds.
Keywords
Cite
@article{arxiv.2404.02535,
title = {Construction of $r$-harmonic submanifolds},
author = {José Miguel Balado-Alves and Anna Siffert},
journal= {arXiv preprint arXiv:2404.02535},
year = {2024}
}
Comments
22 pages, no figures. v2: generalized construction method, addressed corrections, modified exposition