Isoparametric hypersurfaces of a class of Finsler manifolds induced by navigation problem in Minkowski spaces

In this paper, we mainly discuss the isoparametric hypersurfaces of a class of Finsler manifolds (M˜,F˜) produced by navigation datum (F,v), where F is a Minkowski metric. By studying the relationship between the principal curvatures with respect to F˜ and F, we get a general Cartan-type identity an...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 68; p. 101581
Main Authors Dong, Peilong, He, Qun
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2020
Subjects
(dμ-)isoparametric hypersurfaces
Cartan-type identity
Minkowski spaces
Navigation problem
53A10
53C40
(dμ-)isoparametric hypersurfaces
Cartan-type identity
Navigation problem
Minkowski spaces
53C60
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Summary:In this paper, we mainly discuss the isoparametric hypersurfaces of a class of Finsler manifolds (M˜,F˜) produced by navigation datum (F,v), where F is a Minkowski metric. By studying the relationship between the principal curvatures with respect to F˜ and F, we get a general Cartan-type identity and a complete classification of isoparametric hypersurfaces in (M˜,F˜(F,v)). Moreover, for the case v=2cx, when (M˜,F˜) is a Funk-type space with negative constant flag curvature −c2, we also get a complete classification of dμBH-isoparametric hypersurfaces.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2019.101581