| 关于调和映射和全测地映射的一个注记 |
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| 引用本文： | 孙弘安.关于调和映射和全测地映射的一个注记[J].赣南师范学院学报,1990(Z1). |
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| 作者姓名： | 孙弘安 |
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| 作者单位： | 南方冶金学院 |
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| 摘 要： | 本文考虑局部对称的共形平坦黎曼流形,推广了文1]关于调和映射和全测地映射的一个结论。
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| 关 键 词： | 调和映射 全测地映射 局部对称 共形平坦 |
A REMARK ON HARMONIC MAPS AND TOTALLY GEODESIC MAPS |
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| Sun Hongan.A REMARK ON HARMONIC MAPS AND TOTALLY GEODESIC MAPS[J].Journal of Gannan Teachers' College(Social Science(2)),1990(Z1). |
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| Authors: | Sun Hongan |
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| Institution: | southern Institute of Metallurgy |
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| Abstract: | In the present note we prove the following:
Theorem Let f:M~n→M~m be a harmonic and relative affine mapping between Riemannian manifolds, M~m be a locally symetric and conformally flat Riemannian manifold, and M~n be a compact Riemannian manifold with positive Ricci curvatures.If each sectional carvature of M~n is not less
than ?e( f ) K where K is the maximum of the sectional curvatures of M~m, and e ( f ) is the energy density of f, then f is a totally geodesic map. |
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| Keywords: | harmoic map totally geodesic map Iacally symmetric conformally flat |
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