## MAEDA Sadahiro, ADACHI Toshiaki, KIM Young Ho,

## Geodesic spheres in a nonflat complex space form and their integral curves of characteristic vector fields.

## Hokkaido Mathematical Journal, 36 (2007) pp.353-363

### Fulltext

PDF### Abstract

For Hopf hypersurfaces in a nonflat complex space form $M^n(c; \Bbb{C})$, integral curves of their characteristic vector fields are ''nice'' curves in the sense that their extrinsic shapes in $M^n(c; \Bbb{C})$ are K\"ahler circles. In this paper we mainly study geodesic spheres in a nonflat complex space form $M^n(c; \Bbb{C})$. On these geodesic spheres we classify smooth curves whose extrinsic shapes are K\"ahler circles in $M^n(c; \Bbb{C}),c\not=0$. We also give a characterization of complex space forms among K\"ahler manifolds by extrinsic shapes of integral curves of characteristic vector fields on their geodesic spheres.

MSC(Primary) | 53C40 |
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MSC(Secondary) | 53B25 |

Uncontrolled Keywords | complex space forms, geodesic spheres, integral curves of characteristic vector fields, K\"ahler Frenet curves, K\"ahler circles, structure torsion, Hopf hypersurfaces |