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

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

2005-01-25

arxiv.org/abs/math/0501453v1

Mathematics

Differential Geometry

12 pages

Scientific paper

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.

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