Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane (Q1897959)
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scientific article; zbMATH DE number 794611
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane |
scientific article; zbMATH DE number 794611 |
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Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane (English)
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18 September 1995
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Let \(H\) be the Heisenberg group of real upper-triangular \((3 \times 3)\)- matrices with unity entries in the principal diagonal and let \(d_c\) be an arbitrary nonholonomic metric on \(H\). Among other things the author proves that a curve in \((H,d_c)\) starting at the unity \(e \in H\) is a geodesic if and only if it satisfies Pontryagin's maximum principle for an associated time-optimal control problem.
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Minkowski plane
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geodesics
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optimal controls
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Heisenberg group
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