On the Cauchy - Riemann Geometry of Transversal Curves in the 3-Sphere
Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy--Riemann (CR) structure. This paper investigates the CR geometry of curves in $\mathrm S^3$ which are transversal to the contact distribution, using the local CR invariants of $\mathrm S^3$. More specifically, the focus i...
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| Date: | 2020 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2020
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/jm16-0312e |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy--Riemann (CR)
structure. This paper investigates the CR geometry of curves in $\mathrm S^3$
which are transversal to the contact distribution, using the local CR invariants of $\mathrm S^3$.
More specifically, the focus is on the CR geometry of transversal knots.
Four global invariants of transversal knots are considered: the phase anomaly,
the CR spin, the Maslov index, and the CR self-linking number. The interplay between these invariants and the Bennequin number of a knot are discussed.
Next, the simplest CR invariant variational problem for generic transversal curves is considered and its closed critical curves are studied.Mathematics Subject Classification: 53C50, 53C42, 53A10 |
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