| Transformations and non-degenerate maps |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 摘 要： | We shall prove the equivalences of a non-degenerate circle-preserving map and a Mobius transformation in Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn, of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.
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Transformations and non-degenerate maps |
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| Authors: | LI Baokui WANG Yuefei |
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| Abstract: | We shall prove the equivalences of a non-degenerate circle-preserving map and a Mobius transformation in Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn, of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry. |
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| Keywords: | Mobius transformation circle-preserving map non-degenerate map |
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