Semi-invariant submanifolds of codimension 3 satisfying \(\mathfrak{L}_\xi\nabla=0\) in a nonflat complex space form (Q2764634)
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scientific article; zbMATH DE number 1690740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semi-invariant submanifolds of codimension 3 satisfying \(\mathfrak{L}_\xi\nabla=0\) in a nonflat complex space form |
scientific article; zbMATH DE number 1690740 |
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17 February 2003
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real hypersurface, complex space form
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Semi-invariant submanifolds of codimension 3 satisfying \(\mathfrak{L}_\xi\nabla=0\) in a nonflat complex space form (English)
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The title describes the topic in detail. The main result provides a classification of such submanifolds (under additional conditions). The condition \({\mathcal L}_\xi\nabla = 0\) is mysterious for the reviewer: It is explained on page 140 as vanishing derivatives (in the direction of \(\xi\)) of all Christoffel symbols of the Levi-Civita connection on the submanifold. If the reviewer is not wrong, such vanishing condition is not invariant under changes of the coordinate system.
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