Manifold Ways to Darboux-Halphen System

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2018
• Автори: Morales, J.A.C., Movasati, H., Nikdelan, Y., Roychowdhury, R., Torres, M.A.C.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2018
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/209461
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Manifold Ways to Darboux-Halphen System / J.A.C. Morales, H. Movasati, Y. Nikdelan, R. Roychowdhury, M.A.C. Torres // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ.

Many distinct problems give birth to the Darboux-Halphen system of differential equations, and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding an infinite number of double orthogonal surfaces in R³. The second is a problem in general relativity about a gravitational instanton in the Bianchi IX metric space. The third problem stems from the new take on the moduli of enhanced elliptic curves called the Gauss-Manin connection in disguise, developed by one of the authors, and finally, in the last problem Darboux-Halphen system emerges from the associative algebra on the tangent space of a Frobenius manifold.