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Some Problems on Ruled Hypersurfaces in Nonflat Complex Space Forms

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Abstract

We study ruled real hypersurfaces whose shape operators have constant squared norm in nonflat complex space forms. In particular, we prove the nonexistence of such hypersurfaces in the projective case. We also show that biharmonic ruled real hypersurfaces in nonflat complex space forms are minimal, which provides their classification due to a known result of Lohnherr and Reckziegel.

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  1. Department of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain

    Olga Pérez-Barral

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  1. Olga Pérez-Barral
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Correspondence to Olga Pérez-Barral.

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The author acknowledges support by projects MTM2016-75897-P (AEI/FEDER, Spain), PID2019105138GB-C21 (AEI/FEDER, Spain), ED431F 2020/04 (Xunta de Galicia, Spain), and ED431C 2019/10 (Xunta de Galicia, Spain), and by a research grant under the Ramón y Cajal project RYC-2017-22490 (AEI/FSE, Spain).

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Pérez-Barral, O. Some Problems on Ruled Hypersurfaces in Nonflat Complex Space Forms. Results Math 75, 167 (2020). https://doi.org/10.1007/s00025-020-01294-1

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  • DOI: https://doi.org/10.1007/s00025-020-01294-1

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