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Characteristics of T--conformal mappings | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 5، شماره 1، مرداد 2024، صفحه 97-114 اصل مقاله (321.27 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2024.14548.1115 | ||
| نویسندگان | ||
| Mehran Aminian* ؛ Mehran Namjoo | ||
| Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Conformal map؛ Isometry؛ (1,1) --tensor field | ||
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آمار تعداد مشاهده مقاله: 255 تعداد دریافت فایل اصل مقاله: 56 |
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