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- W2896563639 abstract "In this article, we indicate that the open unit ball in n-dimensional Euclidean space $$mathbb {R}^n$$ admits norm-like functions compatible with the Poincaré and Beltrami–Klein metrics. This leads to the notion of a normed gyrogroup, similar to that of a normed group in the literature. We then examine topological and geometric structures of normed gyrogroups. In particular, we prove that the normed gyrogroups are homogeneous and form left invariant metric spaces and derive a version of the Mazur–Ulam theorem. We also give certain sufficient conditions, involving the right-gyrotranslation inequality and Klee’s condition, for a normed gyrogroup to be a topological gyrogroup." @default.
- W2896563639 created "2018-10-26" @default.
- W2896563639 creator A5020758976 @default.
- W2896563639 date "2019-01-01" @default.
- W2896563639 modified "2023-09-26" @default.
- W2896563639 title "On Metric Structures of Normed Gyrogroups" @default.
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- W2896563639 doi "https://doi.org/10.1007/978-3-030-31339-5_20" @default.
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