University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05005120240501Characteristics of T--conformal mappings97114289510.22098/jfga.2024.14548.1115ENMehran AminianDepartment of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran0000-0003-4768-3884Mehran NamjooDepartment of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran0000-0001-5949-6766Journal Article20240130In this paper, we introduce the notion of T-conformal transformations and T-conformal maps between Riemannian manifolds. Here, T stands for a smooth (1,1)-tensor field defined on the domain of these maps. We start by defining what it means for a map to be T-conformal and also dwell on some basic properties of such type maps. We next specialize our discussion to the situation when the map T satisfies the condition ∇T = 0. Accordingly, we prove Liouville's theorem for T-conformal maps between space forms R<sup>n</sup>(c) as an application under the condition ∇T = 0. The proof relies upon properties of T-conformal maps proved earlier. Broadly, the paper seeks to provide a general understanding of conformal mappings in the presence of a tensor field T and show how classical results such as Liouville's theorem apply.https://jfga.uma.ac.ir/article_2895_228313abfd6514f93e9e5d662378f20d.pdf