Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres (Q748926)
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scientific article; zbMATH DE number 4171879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres |
scientific article; zbMATH DE number 4171879 |
Statements
Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres (English)
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1989
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Let B be a submanifold of a Riemannian manifold (M,g), and \(\phi_ B\) the reflection with respect to B, reversing geodesics orthogonal to B on a sufficiently small tubular neighborhood. We derive a characterization of the property that \(\phi_ B\) is isometric by means of the Ricci operator on geodesic spheres tangent to B.
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submanifold
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reflection
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geodesics
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Ricci operator
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