@article{Iqbal2024, 
author = {Muhammad Asad Iqbal and Abid Ali and Ibtesam Alshammari and Cenap Ozel},
title = {Construction of new Lie group and its geometric properties},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {6088-6108},
keywords = {Lie group G, Lie algebra, Lie symmetry, Killing vectors X1, X2 and X3},
url = {https://www.sciopen.com/article/10.3934/math.2024298},
doi = {10.3934/math.2024298},
abstract = {In this paper, we constructed a novel Lie group by using oblate spheroidal coordinates. First, we took the metric tensor of oblate spheroidal coordinates, then found its Killing vectors by using the Killing equation. After solving a system of partial differential equations, we obtained the Killing vectors. With the help of these Killing vectors, we first constructed finite Lie algebra and then proved that Killing vectors form a Lie group. Also, we described the geometric properties in which this Lie group forms a regular surface, defined the differential map and differential of normal vector field, and found the gaussian and mean curvatures.}
}