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.
Citation
Sadahiro MAEDA. Toshiaki ADACHI. Young Ho KIM. "Geodesic spheres in a nonflat complex space form and their integral curves of characteristic vector fields." Hokkaido Math. J. 36 (2) 353 - 363, May 2007. https://doi.org/10.14492/hokmj/1277472808
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