Title: Hamiltonian stability and index of minimal Lagrangian surfaces of the complex projective plane

Authors: Francisco Urbano

Issue: Volume 56 (2007), Issue 2, 931-946

Abstract: We show that the Clifford torus and the totally geodesic real projective plane $\mathbb{R}\mathbb{P}^2$ in the complex projective plane $\mathbb{C}\mathbb{P}^2$ are the unique Hamiltonian stable minimal Lagrangian compact surfaces of $\mathbb{C}\mathbb{P}^2$ with genus $g\leq4$, when the surface is orientable, and with Euler characteristic $\chi\geq-1$, when the surface is nonorientable. Also we characterize $\mathbb{R}\mathbb{P}^2$ in $\mathbb{C}\mathbb{P}^2$ as the least possible index minimal Lagrangian compact nonorientable surface of $\mathbb{C}\mathbb{P}^2$.