Construction of Hamiltonian-stationary Lagrangian submanifolds of constant curvature $\varepsilon$ in complex space forms $\tilde M^n(4\varepsilon)

zbMATH Open1195.53103arXiv1307.3974MaRDI QIDQ4930648

Bang-Yen Chen

Publication date: 1 October 2010

Abstract: Lagrangian submanifolds of a Kaehler manifold are called Hamiltonian-stationary (or $H$-stationary for short) if it is a critical point of the area functional restricted to compactly supported Hamiltonian variations. In [B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, Lagrangian isometric immersions of a real-space-form $M^n(c)$ into a complex-space-form $ilde{M}^n(4c)$, Math. Proc. Cambridge Philo. Soc. 124 (1998), 107-125], an effective method to constructing Lagrangian submanifolds of constant curvature $varepsilon$ in complex space form $M^n(4varepsilon)$ was introduced. In this article we survey recent results on construction of Hamiltonian-stationary Lagrangian submanifolds in complex space forms using this method.

Full work available at URL: https://arxiv.org/abs/1307.3974

Mathematics Subject Classification ID

Global submanifolds (53C40) Lagrangian submanifolds; Maslov index (53D12)

This page was built for publication: Construction of Hamiltonian-stationary Lagrangian submanifolds of constant curvature $\varepsilon$ in complex space forms $\tilde M^n(4\varepsilon)

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4930648)