Agafonov S. Hexagonal geodesic 3-webs (abstract): Difference between revisions
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We present some new local examples of such metrics, discuss known ones, and establish an analogue of the celebrated Graf and Sauer Theorem for Darboux superintegrable metrics. | We present some new local examples of such metrics, discuss known ones, and establish an analogue of the celebrated Graf and Sauer Theorem for Darboux superintegrable metrics. | ||
| slides = | | slides = [[Media:AgafonovTrieste2018slides.pdf|AgafonovTrieste2018slides.pdf]] | ||
| references = {{arXiv|1806.03072}} | | references = {{arXiv|1806.03072}} | ||
| event = [[Local and Nonlocal Geometry of PDEs and Integrability]], 8-12 October 2018, SISSA, Trieste, Italy.<br>''The conference in honor of [[Joseph Krasil'shchik]]'s 70th birthday.'' | | event = [[Local and Nonlocal Geometry of PDEs and Integrability]], 8-12 October 2018, SISSA, Trieste, Italy.<br>''The conference in honor of [[Joseph Krasil'shchik]]'s 70th birthday.'' | ||
| 79YY-MM-DD = 7981-89-90 | | 79YY-MM-DD = 7981-89-90 | ||
}} | }} | ||
Latest revision as of 09:01, 31 October 2018
Speaker: Sergey Agafonov
Title: Hexagonal geodesic 3-webs
Abstract:
We prove that a surface carries a hexagonal 3-web of geodesics if and only if the geodesic flow on the surface admits a cubic first integral and show that the system of partial differential equations, governing metrics on such surfaces, is integrable by generalized hodograph transform method.
We present some new local examples of such metrics, discuss known ones, and establish an analogue of the celebrated Graf and Sauer Theorem for Darboux superintegrable metrics.
Slides: AgafonovTrieste2018slides.pdf
References:
arXiv:1806.03072
Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.