Instability for harmonic foliations on compact homogeneous spaces |
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Authors: | Kei Ichikawa |
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Institution: | a Kawagoe Senior High School, 2-6 Kuruwa, Kawagoe, Saitama 350-0053, Japan b Osaka City University, Advanced Mathematical Institute, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan |
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Abstract: | In this paper we discuss the instability of harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact homogeneous spaces. We obtain a sufficient condition for a harmonic foliation to be unstable on compact submanifolds in a Euclidean space and on compact isotropy irreducible homogeneous spaces. We also classify compact symmetric spaces which have no non-trivial stable harmonic foliation. |
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Keywords: | primary 53C12 secondary 57R30 |
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