Remarks on projectively invariant nonlinear partial differential equations (Q1101971)
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scientific article; zbMATH DE number 4048567
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remarks on projectively invariant nonlinear partial differential equations |
scientific article; zbMATH DE number 4048567 |
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Remarks on projectively invariant nonlinear partial differential equations (English)
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1988
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In this note it is pointed out how positive solutions of the equations det hess v\(=v^{-(n+2)}\) and det hess v\(=-v^{-(n+2)}\) generate metrics invariant under projective transformations. For standard canonical domains these metrics are correspondingly the standard Riemannian metric of constant sectional curvature 1 and the pseudo-Riemannian metric of sectional curvature 1.
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projectively invariant metrics
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projective transformations
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constant sectional curvature
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