A Santalo's formula in L-P (Q1118181)
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scientific article; zbMATH DE number 4094322
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Santalo's formula in L-P |
scientific article; zbMATH DE number 4094322 |
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A Santalo's formula in L-P (English)
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1989
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The upper half plane \(y>0\) with the metric \(ds^ 2=(dx^ 2-dy^ 2)y^{-2}\) is called L-P plane or simply L-P. The curvature of L-P is 1. There are obtained some expressions for the density of points, pair of points, geodesics, pairs of geodesics and the kinematic density. The author shows that an integral formula by L. A. Santaló on hyperbolic space of curvature -1 holds for the L-P plane.
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L-P plane
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density of points
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geodesics
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kinematic density
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0.8053092360496521
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0.741828978061676
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