Abstract
On every isoparametric submanifold M a connection with parallel second fundamental form is constructed geometrically such that M is an orbit of an s-representation if and only if the connection is a canonical one. If the rank of M is greater than one this connection is in case of homogeneity the canonical connection of the reductive decomposition given by the orbit of s-representation.
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Leschke, K. Homogeneity and Canonical Connections of Isoparametric Manifolds. Annals of Global Analysis and Geometry 15, 51–69 (1997). https://doi.org/10.1023/A:1006585108364
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DOI: https://doi.org/10.1023/A:1006585108364