Harmonic \(\varphi\)-morphisms (Q1403497)
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scientific article; zbMATH DE number 1973827
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Harmonic \(\varphi\)-morphisms |
scientific article; zbMATH DE number 1973827 |
Statements
Harmonic \(\varphi\)-morphisms (English)
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2 September 2003
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The authors characterize the harmonicity of \(\varphi\)-morphisms \(\Phi:TM\rightarrow TN\) which cover a map \(\varphi:M\rightarrow N\) between manifolds, when the tangent bundles carry the complete metric. Among numerous other results, it is proved that the mapping \(\varphi\) is a harmonic morphism iff \(d\varphi\) is a harmonic \(\varphi\)-morphism. Examples and applications to \((1,1)\)-tensor fields are provided as well.
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harmonic morphism
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harmonic map
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complete lift metric
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tangent bundle
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\(\varphi\)-morphism
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