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.
Aminian, M., & Namjoo, M. (2024). Characteristics of T--conformal mappings. Journal of Finsler Geometry and its Applications, (), 97-114. doi: 10.22098/jfga.2024.14548.1115
MLA
Mehran Aminian; Mehran Namjoo. "Characteristics of T--conformal mappings". Journal of Finsler Geometry and its Applications, , , 2024, 97-114. doi: 10.22098/jfga.2024.14548.1115
HARVARD
Aminian, M., Namjoo, M. (2024). 'Characteristics of T--conformal mappings', Journal of Finsler Geometry and its Applications, (), pp. 97-114. doi: 10.22098/jfga.2024.14548.1115
VANCOUVER
Aminian, M., Namjoo, M. Characteristics of T--conformal mappings. Journal of Finsler Geometry and its Applications, 2024; (): 97-114. doi: 10.22098/jfga.2024.14548.1115