Totally geodesic foliations and Killing fields. II (Q1070544)
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scientific article; zbMATH DE number 3937981
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Totally geodesic foliations and Killing fields. II |
scientific article; zbMATH DE number 3937981 |
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Totally geodesic foliations and Killing fields. II (English)
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1986
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The author extends his results in part I [ibid. 35, 387-392 (1983; Zbl 0517.53035)] to higher codimensions as follows: Theorem. Let (M,g) be a connected complete Riemannian manifold and F be a totally geodesic foliation of (M,g). Assume that the bundle orthogonally complement to F is also integrable. Then any Killing field Z on (M,g) with bounded length, i.e., \(g(Z,Z)\leq const.<\infty\) on M, preserves F. Further, he studies a related topic concerning minimal foliations.
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totally geodesic foliation
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Killing field
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minimal foliations
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