## 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

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.
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.