TY - JOUR
ID - 2895
TI - Characteristics of T--conformal mappings
JO - Journal of Finsler Geometry and its Applications
JA - JFGA
LA - en
SN -
AU - Aminian, Mehran
AU - Namjoo, Mehran
AD - Department of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
Y1 - 2024
PY - 2024
VL - 5
IS - 1
SP - 97
EP - 114
KW - Conformal map
KW - Isometry
KW - (1
KW - 1)–tensor field
DO - 10.22098/jfga.2024.14548.1115
N2 - 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.
UR - https://jfga.uma.ac.ir/article_2895.html
L1 - https://jfga.uma.ac.ir/article_2895_228313abfd6514f93e9e5d662378f20d.pdf
ER -