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.
Publié le : 2007-05-15
Classification:
complex space forms,
geodesic spheres,
integral curves of characteristic vector fields,
K\"ahler Frenet curves,
K\"ahler circles,
structure torsion,
Hopf hypersurfaces,
53C40,
53B25
@article{1277472808,
author = {MAEDA, Sadahiro and ADACHI, Toshiaki and KIM, Young Ho},
title = {Geodesic spheres in a nonflat complex space form and their integral curves of characteristic vector fields},
journal = {Hokkaido Math. J.},
volume = {36},
number = {4},
year = {2007},
pages = { 353-363},
language = {en},
url = {http://dml.mathdoc.fr/item/1277472808}
}
MAEDA, Sadahiro; ADACHI, Toshiaki; KIM, Young Ho. Geodesic spheres in a nonflat complex space form and their integral curves of characteristic vector fields. Hokkaido Math. J., Tome 36 (2007) no. 4, pp. 353-363. http://gdmltest.u-ga.fr/item/1277472808/