A short note on biharmonic submanifolds in 3-dimensional generalized $(kappa, mu)$-manifolds

摘要

We characterize proper biharmonic anti-invariant surfaces in $3$-dimensional generalized $(kappa, mu)$-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain $3$-dimensional generalized $(kappa, mu)$-manifold. Moreover, we determine $3$-dimensional generalized $(kappa, mu)$-manifolds which admit a certain kind of proper biharmonic foliation.