A splitting theorem for higher order parallel immersions (Q2845561)
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scientific article; zbMATH DE number 6203555
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A splitting theorem for higher order parallel immersions |
scientific article; zbMATH DE number 6203555 |
Statements
A splitting theorem for higher order parallel immersions (English)
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2 September 2013
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parallel immersions
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\(k\)-parallel immersions
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space form
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flat spaces
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flat normal bundles
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splitting theorems
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The authors first introduce the notions that we will meet in the article in the context of existing results. Then they demonstrate some technical lemmas and propositions. The main result of the article is the following theorem: NEWLINENEWLINELet \((M; g)\rightarrow M^n(c)\) be a \(k\)-parallel isometric immersion into a standard space form \(M^n(c)\) of sectional curvature \(c\). It is the local product of a parallel immersion and a \(k\)-parallel immersion of a flat space with flat normal bundle. When \((M; g)\) is simply connected and complete, then the splitting is global.
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