Abstract
It is straightforward to show that any non-degenerate hypersurface with a relative normal and parallel shape operator with respect to that normal must be locally ruled if it is not a hypersphere. We give a precise local description for this class in dimensions two and three.
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Binder, T. On relative hypersurfaces with parallel shape operator. Results. Math. 46, 227–236 (2004). https://doi.org/10.1007/BF03322884
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DOI: https://doi.org/10.1007/BF03322884