Construction of Hamiltonian-stationary Lagrangian submanifolds of constant curvature ε in complex space forms Mⁿ(4ε)

2013/07/15 by Chen, Bang-Yen
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.3974

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 Mⁿ(c) into a complex-space-form Mⁿ(4c), Math. Proc. Cambridge Philo. Soc. 124 (1998), 107-125], an effective method to constructing Lagrangian submanifolds of constant curvature ε in complex space form Mⁿ(4ε) was introduced. In this article we survey recent results on construction of Hamiltonian-stationary Lagrangian submanifolds in complex space forms using this method.

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