Geodesic
HYPERSURFACES IN ${\mathbb C}$P2 AND ${\mathbb C}$H2 WITH TWO DISTINCT PRINCIPAL CURVATURES
Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 137-152

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DOI

It is known that hypersurfaces in ${\mathbb C}$Pn or ${\mathbb C}$Hn for which the number g of distinct principal curvatures satisfies g ≤ 2, must belong to a standard list of Hopf hypersurfaces with constant principal curvatures, provided that n ≥ 3. In this paper, we construct a two-parameter family of non-Hopf hypersurfaces in ${\mathbb C}$P2 and ${\mathbb C}$H2 with g=2 and show that every non-Hopf hypersurface with g=2 is locally of this form. 
IVEY, THOMAS A.; RYAN, PATRICK J. HYPERSURFACES IN ${\mathbb C}$P2 AND ${\mathbb C}$H2 WITH TWO DISTINCT PRINCIPAL CURVATURES. Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 137-152. doi: 10.1017/S0017089515000105
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     author = {IVEY, THOMAS A. and RYAN, PATRICK J.},
     title = {HYPERSURFACES {IN} ${\mathbb C}${P2} {AND} ${\mathbb C}${H2} {WITH} {TWO} {DISTINCT} {PRINCIPAL} {CURVATURES}},
     journal = {Glasgow mathematical journal},
     pages = {137--152},
     year = {2016},
     volume = {58},
     number = {1},
     doi = {10.1017/S0017089515000105},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000105/}
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