Hamiltonian stability and index of minimal Lagrangian surfaces of the complex projective plane
Differential Geometry
2007-05-23 v1 Symplectic Geometry
Abstract
We show that the Clifford torus and the totally geodesic real projective plane RP^2 in the complex projective plane CP^2 are the unique Hamiltonian stable minimal Lagrangian compact surfaces of CP^2 with genus less than or equal to 4, when the surface is orientable, and with Euler characteristic greater than or equal to -1, when the surface is nonorientable. Also we characterize RP^2 in CP^2 as the least possible index minimal Lagrangian compact nonorientable surface of CP^2.
Keywords
Cite
@article{arxiv.math/0501453,
title = {Hamiltonian stability and index of minimal Lagrangian surfaces of the complex projective plane},
author = {Francisco Urbano},
journal= {arXiv preprint arXiv:math/0501453},
year = {2007}
}
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12 pages