Let (M,F,g0) be a Riemannian minimal foliation. The transverse Yamabe problem is to find a metric g in the basic conformal class of g0 such that the transverse scalar curvature of g is constant. We first study the uniqueness of the solutions of the transverse Yamabe problem. As a generalization of the transverse Yamabe problem, we study the problem of prescribing transverse scalar curvature by using geometric flow. We then prove a version of conformal Schwarz lemma on (M,F,g0) . Finally, we consider the transverse Yamabe soliton, which is the self-similar solution of the transverse Yamabe flow.
Relation:
International Journal of Mathematics 33(14), 2250091
