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Classification of isoparametric hypersurfaces in spheres with $ (g,m)=(6,1)$


Author: Anna Siffert
Journal: Proc. Amer. Math. Soc. 144 (2016), 2217-2230
MSC (2010): Primary 53C40; Secondary 53C55, 53C30
DOI: https://doi.org/10.1090/proc/12924
Published electronically: October 8, 2015
MathSciNet review: 3460180
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Abstract: We classify the isospectral families $ L(t)=\cos (t)L_0+\sin (t)L_1\in$$ \mbox {Sym}(5,\mathbb{R})$, $ t\in \mathbb{R}$, with $ L_0=$$ \mbox {diag}(\sqrt {3},\tfrac {1}{\sqrt {3}},0, -\tfrac {1}{\sqrt {3}},-\sqrt {3})$. Using this result we provide a classification of isoparametric hypersurfaces in spheres with $ (g,m)=(6,1)$ and thereby give a simplified proof of the fact that any isoparametric hypersurface with $ (g,m)=(6,1)$ is homogeneous. This result was first proven by Dorfmeister and Neher in 1985.


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Additional Information

Anna Siffert
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Email: asiffert@math.upenn.edu

DOI: https://doi.org/10.1090/proc/12924
Received by editor(s): April 9, 2015
Received by editor(s) in revised form: June 16, 2015
Published electronically: October 8, 2015
Additional Notes: The author would like to thank DFG for supporting this work with the grant SI 2077/1-1.
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society

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