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Complete real hypersurfaces in compact rank one symmetric spaces
Author(s):
Tatsuyoshi
Hamada;
Katsuhiro
Shiohama
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3905-3910.
MSC (2000):
Primary 53C20, 53C40
Posted:
June 9, 2009
MathSciNet review:
2529899
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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
DOI:
10.1090/S0002-9939-09-09959-6
PII:
S 0002-9939(09)09959-6
Received by editor(s):
October 15, 2008,
Received by editor(s) in revised form:
March 7, 2009
Posted:
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 of article:
Copyright
2009,
American Mathematical Society
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