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

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 ${\tilde{M}}^n(4c)$, Math. Proc. Cambridge Philo. Soc. 124 (1998), 107-125], an effective method to constructing Lagrangian submanifolds of constant curvature $\epsilon$ in complex space form $M^n(4\epsilon )$ was introduced. In this article we survey recent results on construction of Hamiltonian-stationary Lagrangian submanifolds in complex space forms using this method.

24 pages. Appeared in Bull. Transilv. Univ. Brasov Ser. B (N.S.) 14(49) (2007), suppl., 51-74

References in corpus (1)

• Hamiltonian stationary tori in the complex projective plane