Abstract
We consider proper Dupin hypersurfaces of the Euclidean space \(\mathbb {R}^{n+1}\), that admit principal coordinate systems and have n distinct nonvanishing principal curvatures. We obtain explicitly all such hypersurfaces that have constant Laguerre curvatures. In particular, we show that they are determined by \(n-2\) Laguerre curvatures and two other constants, one of them being nonzero.
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Partially supported by CNPq, Ministry of Science and Technology, Brazil, Proc. 312462/2014-0.
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Cezana, M., Tenenblat, K. Dupin hypersurfaces with constant Laguerre curvatures. manuscripta math. 154, 169–184 (2017). https://doi.org/10.1007/s00229-017-0915-x
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DOI: https://doi.org/10.1007/s00229-017-0915-x