Examples of Hamiltonian-minimal Lagrangian submanifolds in $\operatorname{Gr}(r, n)$
- Authors: Tyurin N.A.1,2
-
Affiliations:
- Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow Region
- National Research University Higher School of Economics, Moscow
- Issue: Vol 89, No 2 (2025)
- Pages: 146-160
- Section: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/303951
- DOI: https://doi.org/10.4213/im9599
- ID: 303951
Cite item
Open Access
Access granted
Subscription Access
Abstract
We extend the A. E. Mironov's construction of (Hamiltonian)-minimal Lagrangian submanifolds tothe case of an algebraic manifold that can be equipped with a Kahler–Einstein metricsymmetric under the action of the torus $T^k$. As an application, we give examples of Hamiltonian-minimalLagrangian submanifolds of the Grassmannian $\operatorname{Gr}(r, n)$.
About the authors
Nikolai Andreevich Tyurin
Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow Region; National Research University Higher School of Economics, Moscow
Author for correspondence.
Email: bltp@thsun1.jinr.ru
Doctor of physico-mathematical sciences, Professor
References
- А. Е. Миронов, “О новых примерах гамильтоново-минимальных и минимальных лагранжевых подмногообразий в $mathbb{C}^n$ и $mathbb{C}mathrm{P}^n$”, Матем. сб., 195:1 (2004), 89–102
- Yong-Geun Oh, “Volume minimization of Lagrangian submanifolds under Hamiltonian deformations”, Math. Z., 212:2 (1993), 175–192
- Н. A. Тюрин, “Лагранжевы циклы Миронова в алгебраических многообразиях”, Матем. сб., 212:3 (2021), 128–138
- Н. A. Тюрин, “Примеры циклов Миронова в многообразиях Грассмана”, Сиб. матем. журн., 62:2 (2021), 457–465
- Н. А. Тюрин, “Симплектическая редукция и лагранжевы подмногообразия в $operatorname{Gr}(1, n)$”, Матем. сб., 215:10 (2024), 167–182
- Ф. Гриффитс, Дж. Харрис, Принципы алгебраической геометрии, Мир, М., 1982, 864 с.
- M. Audin, Torus actions on symplectic manifolds, Progr. Math., 93, 2nd rev. ed., Birkhäuser Verlag, Basel, 2004, viii+325 pp.
- П. Е. Пушкарь, “Лагранжевы пересечения в симплектическом пространстве”, Функц. анализ и его прил., 34:4 (2000), 64–70
- I. M. Gelfand, R. D. MacPherson, “Geometry in Grassmannians and a generalization of the dilogarithm”, Adv. Math., 44:3 (1982), 279–312
Supplementary files
