| 垂直调和映射的二阶变分 |
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| 引用本文： | 蔡开仁,刘继志.垂直调和映射的二阶变分[J].北京师范大学学报(自然科学版),1993,29(4):443-446. |
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| 作者姓名： | 蔡开仁 刘继志 |
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| 作者单位： | 北京师范大学数学系，北京师范大学数学系 100875 北京，100875 北京 |
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| 摘 要： | 对于黎曼流形的浸没建立了垂直能量泛函的二阶变分公式，研究强垂直调和映射的稳定性。得到球面和球面中某些子流形任意黎曼流形的非平凡的稳定强垂直调和映射的不存在性定理。
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| 关 键 词： | 调和映射 浸没 稳定性 二阶变分 |
THE SECOND VARIATION FOR VERTICAL HARMONIC MAP |
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| Cai Kairen Liu Jizhi.THE SECOND VARIATION FOR VERTICAL HARMONIC MAP[J].Journal of Beijing Normal University(Natural Science),1993,29(4):443-446. |
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| Authors: | Cai Kairen Liu Jizhi |
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| Abstract: | The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner. It is proved that any non-trivial strong vertical harmonic map from the Euclidean sphere to a Riemannian manifold is unstable. This generilized the results due to Wood, Mazet and Xin. |
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| Keywords: | harmonic map submersion stability |
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