Abstract
We characterize isometric vector fields through a distance resembling the Gromov–Hausdorff one (Burago D, Burago Y, Ivanov S in A course in metric geometry. Graduate studies in mathematics, vol 33, American Mathematical Society, Providence, 2001). We then use this distance to generate a metrizable topology in the space of vector fields on closed manifolds up to isometry. We prove that the set of Killing vector fields is closed with respect to this topology.
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Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
JL was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A6A3A01091340). CAM was partially supported by CNPq-Brazil and the NRF Brain Pool Grant funded by the Korea government (No. 2020H1D3A2A01085417).
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Lee, J., Morales, C.A. Isometric vector fields from the Gromov–Hausdorff viewpoint. J. Geom. 112, 42 (2021). https://doi.org/10.1007/s00022-021-00609-z
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DOI: https://doi.org/10.1007/s00022-021-00609-z
Keywords
- Vector field
- Gromov–Hausdorff distance
- closed manifold
- isometry
- \(\epsilon \)-isometry
- killing vector field