Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups
Differential Geometry
2016-12-06 v1
Abstract
We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we determine all the proper biharmonic submanifolds in irreducible symmetric spaces of compact type which are singular orbits of commutative Hermann actions of cohomogeneity two. Also, in compact simple Lie groups, we determine all the biharmonic hypersurfaces which are regular orbits of actions of the direct product of two symmetric subgroups which are associated to commutative Hermann actions of cohomogeneity one.
Keywords
Cite
@article{arxiv.1612.01063,
title = {Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups},
author = {Shinji Ohno and Takashi Sakai and Hajime Urakawa},
journal= {arXiv preprint arXiv:1612.01063},
year = {2016}
}
Comments
53 pages. arXiv admin note: text overlap with arXiv:1507.01738