Abstract
We consider isometric immersions F: M → \(\tilde M\) between Riemannian manifolds whose higher mean curvature forms [in the sense of the author, Manuscripta Math. 49 (1984), 177–194] are all (covariantly) constant or, equivalently, whose shape operator with respect to each parallel unit normal vector field along any curve in M has constant eigenvalues. As in the hypersurface case we call such immersions isoparametric. Among other results it is proved: Isoparametric surfaces of constant curvature spaces are symmetric, i.e. have parallel second fundamental form. The same is true for isoparametric Kählerian hypersurfaces of complex space forms.
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Strübing, W. Isoparametric submanifolds. Geom Dedicata 20, 367–387 (1986). https://doi.org/10.1007/BF00149586
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DOI: https://doi.org/10.1007/BF00149586