Stefan Andronic, Yu Fu, Cezar Oniciuc: On the biharmonic hypersurfaces with three distinct principal curvatures in space forms, 35-58

Abstract:

In [19] the author proved that any hypersurface with at most three distinct principal curvatures in space forms has constant mean curvature. Recently, we found out that the proof given in [19] has a gap which we fill in the present paper. More specifically, in order to overcome this problem, we introduce a new method involving algebraic tools and Mathematica programming. We manage to find all cases that the original proof missed and show that all hypersurfaces of this type still have constant mean curvature.

Key Words: Biharmonic hypersurfaces, mean curvature, space forms.

2020 Mathematics Subject Classification: Primary 53C42; Secondary 53B25.

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