On deformation of Riemannian metrics quadratic in the Ricci tensor (Q1760525)
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scientific article; zbMATH DE number 6105699
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On deformation of Riemannian metrics quadratic in the Ricci tensor |
scientific article; zbMATH DE number 6105699 |
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On deformation of Riemannian metrics quadratic in the Ricci tensor (English)
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14 November 2012
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The author proves the short-time existence of solution of the following quadratic flow \[ \frac{\partial g_{ij}}{\partial t}=-2R_{ij}+\lambda (x)R_i^lR_{lj} \] on compact manifold \(M\) when the function \(\lambda\in C^{\infty}(M)\) is sufficiently small in \(L^{\infty}\) norm. They also construct formulas of the deformation of the Ricci tensor for this flow.
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Riemannian metric
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Ricci curvature
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De Turk trick
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linearization
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