%0 Journal Article
%T Characteristics of T--conformal mappings
%J Journal of Finsler Geometry and its Applications
%I University of Mohaghegh Ardabili
%Z 2783-0500
%A Aminian, Mehran
%A Namjoo, Mehran
%D 2024
%\ 05/01/2024
%V 5
%N 1
%P 97-114
%! Characteristics of T--conformal mappings
%K Conformal map
%K Isometry
%K (1
%K 1)–tensor field
%R 10.22098/jfga.2024.14548.1115
%X In 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 Rn(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.
%U https://jfga.uma.ac.ir/article_2895_228313abfd6514f93e9e5d662378f20d.pdf