Tohoku Mathematical Journal
2008
December
SECOND SERIES VOL. 60, NO. 4

Tohoku Math. J.
60 (2008), 597-605

Title EXTRINSIC GEODESICS AND HYPERSURFACES OF TYPE (A) IN A COMPLEX PROJECTIVE SPACE

Dedicated to Professor Kouei Sekigawa on the occasion of his retirement from Niigata University
Author Sadahiro Maeda and Toshiaki Adachi

(Received March 21, 2008)
Abstract. In a complex projective space, we distinguish hypersurfaces of type $({\rm A}_1)$ from hypersurfaces of type $({\rm A}_2)$ in terms of the cardinality of congruence classes of their extrinsic geodesics.

2000 Mathematics Subject Classification. Primary 53B25; Secondary 53C40.
Key words and phrases. Hypersurfaces of type (A), geodesic spheres, hypersurfaces of type $({\rm A}_2)$, ruled real hypersurfaces, complex projective spaces, normal section, integral curves of the characteristic vector field, geodesics, extrinsic geodesics, structure torsion, normal curvature.

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