On geodesics which intersect a convex domain of nonpositive curvature (Q1209813)
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scientific article; zbMATH DE number 168577
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On geodesics which intersect a convex domain of nonpositive curvature |
scientific article; zbMATH DE number 168577 |
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On geodesics which intersect a convex domain of nonpositive curvature (English)
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16 May 1993
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The author shows that for a simply connected complete Riemannian manifold \(X\) of nonpositive curvature the space of oriented geodesics is an exact symplectic variety and the measure of geodesics of \(X\) intersecting a convex region \(K\) is given by the surface area of \(\partial K\) times the volume of the \((n -1)\)-dimensional unit ball.
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space of oriented geodesics
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measure of geodesics
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surface area
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0.7548708319664001
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0.7433068156242371
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0.7433068156242371
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