A Schwarz lemma for transversally V-harmonic maps between Riemannian foliated manifolds

In this paper, we prove a transversal V-Laplacian comparison theorem under a transversal Bakry-Emery Ricci condition. We establish a Schwarz type lemma for transversally V-harmonic maps of bounded generalized transversal dilatation between Riemannian foliated manifolds by using this comparison theorem, including for the case of \(V = \nabla^{\mathcal{H}} h\) $$V={\mathrm{\nabla }}^{\mathcal{H}}h$$ .