The algebraic sets of vectors generating planar normal sections of isoparametric hypersurfaces of FKM type

Authors

  • Cristián U. Sánchez CIEM–CONICET and Fa.M.A.F., Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina

DOI:

https://doi.org/10.33044/revuma.2279

Abstract

We present a proof of the connectedness of the algebraic set of vectors generating planar normal sections for all isoparametric hypersurfaces, with positive multiplicities $m_{1}$ and $m_{2}$ of FKM type.

 

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References

T. E. Cecil and P. J. Ryan, Geometry of Hypersurfaces, Springer Monographs in Mathematics, Springer, New York, 2015. MR 3408101.

D. Ferus, H. Karcher, and H. F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981), no. 4, 479–502. MR 0624227. Unofficial English translation available at https://arxiv.org/abs/1112.2780 [math.DG], 2011.

C. U. Sánchez, Algebraic sets associated to isoparametric submanifolds, in New Developments in Lie Theory and Geometry, 37–56, Contemp. Math., 491, Amer. Math. Soc., Providence, RI, 2009. MR 2537050.

C. U. Sánchez, Connectedness of the algebraic set of vectors generating planar normal sections of homogeneous isoparametric hypersurfaces, Rev. Un. Mat. Argentina 58 (2017), no. 1, 53–75. MR 3665898.

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Published

2022-12-12

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