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

2005/01/25 by Francisco Urbano, Urbano, Francisco
Mathematics · #49Q20 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:49Q20 #msc:53A10

paper · pdf · doi:10.48550/arxiv.math/0501453

12 pages

arxiv created 2005/01/25 · arxiv updated 2009/12/01

Abstract

We show that the Clifford torus and the totally geodesic real projective plane RP² in the complex projective plane CP² are the unique Hamiltonian stable minimal Lagrangian compact surfaces of CP² 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 RP² in CP² as the least possible index minimal Lagrangian compact nonorientable surface of CP².

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