Publication: The flag curvature of a submanifold
of a Randers–Minkowski space in terms of Zermelo data
Authors
Huber, Matthieu ; Javaloyes Victoria, Miguel Ángel
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Publisher
Springer
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DOI
https://doi.org/10.1007/s00025-022-01661-0
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info:eu-repo/semantics/article
Description
© 2022, The Author(s). This manuscript version is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by/4.0/
This document is the Published Manuscript, version of a Published Work that appeared in final form in Results in Mathematics. To access the final edited and published work see https://doi.org/10.1007/s00025-022-01661-0
Abstract
The main result of this paper is an expression of the flag curvature of a submanifold of a Randers–Minkowski space (V , F ) in terms of invariants related to its Zermelo data (h, W ). More precisely, these invariants are the sectional curvature and the second fundamental form of the positive definite scalar product h and some projections of the wind W. This expression allows for a promising characterization of submanifolds with scalar flag curvature in terms of Riemannian quantities, which, when a hypersurface is considered, seems quite approachable. As a consequence, we prove that any h-flat hypersurface S has scalar F-flag curvature and the metric of its Zermelo data is conformally flat. As a tool for making the computation, we previously reobtain the Gauss–Codazzi equations of a pseudo-Finsler submanifold using anisotropic calculus.
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Citation
Results in Mathematics, 2022, Vol. 77 : 124
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