Classification of isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$
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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.References
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Additional Information
- Anna Siffert
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- MR Author ID: 1060420
- Email: asiffert@math.upenn.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2217-2230
- MSC (2010): Primary 53C40; Secondary 53C55, 53C30
- DOI: https://doi.org/10.1090/proc/12924
- MathSciNet review: 3460180