## Tohoku Mathematical Journal 2005 June SECOND SERIES VOL. 57, NO. 2

 Tohoku Math. J. 57 (2005), 223-230

Title REAL HYPERSURFACES SOME OF WHOSE GEODESICS ARE PLANE CURVES IN NONFLAT COMPLEX SPACE FORMS

Author Toshiaki Adachi, Makoto Kimura and Sadahiro Maeda

(Received July 23, 2003, revised April 1, 2004)
Abstract. In this paper we classify real hypersurfaces all of whose geodesics orthogonal to the characteristic vector field are plane curves in complex projective or complex hyperbolic spaces.

2000 Mathematics Subject Classification. Primary 53B25; Secondary 53C40.

Key words and phrases. Real hypersurfaces, nonflat complex space forms, geodesics, plane curves, curves of order 2, totally $\eta$-umbilic, ruled real hypersurfaces.

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