arXiv subjects
Publications and source records attributed to Jungwoo Moon.
We investigate a compact Einstein-type manifold whose potential vector field generates a Riemannian foliation. In particular, we prove necessary conditions for such a manifold to be taut and to have a splitting property. Additionally, some properties of taut Riemannian foliations on a compact almost Ricci solitons and a compact Einstein manifolds are provided.
We study tautness properties of a Riemannian foliation by investigating a symmetric 2-tensor associated with the mean curvature of the foliation. As a consequence, we prove a tautness condition for Riemannian foliations on compact manifolds via the symmetric tautness tensor. Moreover, several applications of the aforementioned tensor are provided under various geometric conditions.
We investigate transverse Ricci solitons, the self-similar solutions of the transverse Ricci flow, on a compact foliated manifold. In particular, we show the relations between a taut Riemannian foliation and a transverse Ricci soliton. Moreover, we find some examples of transverse Ricci solitons.