Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups

Abstract

We give a necessary and su‰cient 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 orbits of these Lie group actions under some additional settings. As a consequence, we obtain many examples of proper biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups.