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

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.

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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

Information

Published: May 2007
First available in Project Euclid: 25 June 2010

zbMATH: 1139.53007
MathSciNet: MR2347430
Digital Object Identifier: 10.14492/hokmj/1277472808

Subjects:
Primary: 53C40
Secondary: 53B25

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics

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Vol.36 • No. 2 • May 2007
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