Symplectomorphic codimension 1 totally geodesic submanifolds (Q1842136)
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scientific article; zbMATH DE number 743990
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symplectomorphic codimension 1 totally geodesic submanifolds |
scientific article; zbMATH DE number 743990 |
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Symplectomorphic codimension 1 totally geodesic submanifolds (English)
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3 August 1995
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We show that the coisotropic totally geodesic properly embedded submanifolds of codimension 1 of a simply connected complete Kähler manifold of non-positive sectional curvature are symplectically linearizable. First we show that such a submanifold is foliated by totally geodesic complex leaves transversal to an isometric flow, hence, by a result of E. Ghys, is a Riemannian product. We then apply a result of B. Reinhart concerning bundle like metrics.
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symplectic
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coisotropic
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