Complete real hypersurfaces in compact rank one symmetric spaces
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- by Tatsuyoshi Hamada and Katsuhiro Shiohama PDF
- Proc. Amer. Math. Soc. 137 (2009), 3905-3910 Request permission
Abstract:
The local classification of real hypersurfaces in a compact rank one symmetric space has been investigated by many people. Making use of the global behavior of geodesics on CROSS, we prove that a complete real hypersurface in a CROSS is a metric sphere if its shape operator and the curvature transformation with respect to the normal have the same eigenspaces at each point of it and if its principal curvatures are constant. We emphasize that our discussion is independent of the choice of the coefficient fields of projective spaces with constant holomorphic sectional curvature.References
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Additional Information
- Tatsuyoshi Hamada
- Affiliation: Department of Applied Mathematics, Faculty of Sciences, Fukuoka University, 8-19-1 Nanakuma, Fukuoka, 814-0180, Japan – and – Japan Science and Technology Agency, CREST, 5, Sanbancho, Chiyoda-ku, Tokyo, 102-0075, Japan
- Email: hamada@holst.sm.fukuoka-u.ac.jp
- Katsuhiro Shiohama
- Affiliation: Department of Applied Mathematics, Faculty of Sciences, Fukuoka University, 8-19-1 Nanakuma, Fukuoka, 841-0180, Japan
- MR Author ID: 160870
- Received by editor(s): October 15, 2008
- Received by editor(s) in revised form: March 7, 2009
- Published electronically: June 9, 2009
- Additional Notes: The research of the first-named author was partially supported by Grant-in-Aid for Scientific Research (C), No. 18540104. The research of the second-named author was partially supported by Grant-in-Aid for Scientific Research (C), No. 19540107
- Communicated by: Jon G. Wolfson
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 3905-3910
- MSC (2000): Primary 53C20, 53C40
- DOI: https://doi.org/10.1090/S0002-9939-09-09959-6
- MathSciNet review: 2529899