On the topology of isoparametric hypersurfaces with four distinct principal curvatures
نویسندگان
چکیده
منابع مشابه
Principal Curvatures of Isoparametric Hypersurfaces in Cp
Let M be an isoparametric hypersurface in CPn, and M the inverse image of M under the Hopf map. By using the relationship between the eigenvalues of the shape operators of M and M , we prove that M is homogeneous if and only if either g or l is constant, where g is the number of distinct principal curvatures of M and l is the number of non-horizontal eigenspaces of the shape operator on M .
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In [6], employing commutative algebra, we showed that if the number of principal curvatures is 4 and if the multiplicities m1 and m2 of the principal curvatures satisfy m2 ≥ 2m1 − 1, then the isoparametric hypersurface is of the type constructed by Ozeki-Takeuchi and Ferus-Karcher-Münzner [18], [11]. This leaves only four multiplicity pairs (m1, m2) = (3, 4), (4, 5), (6, 9) and (7, 8) unsettled...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04490-1