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Cauchy–Riemann equations and J-symplectic forms |
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| Authors: | R Ferreiro Prez J Muoz Masqu |
| Institution: | aDepartamento de Economía Financiera y Contabilidad I, Facultad de Ciencias Económicas y Empresariales, Universidad Complutense de Madrid, Campus de Somosaguas, 28223-Pozuelo de Alarcón, Spain bInstituto de Física Aplicada, CSIC, C/ Serrano 144, 28006-Madrid, Spain |
| Abstract: | Let (Σ,j) be a Riemann surface. The almost complex manifolds (M,J) for which the J-holomorphic curves  :Σ→M are of variational type, are characterized. This problem is related to the existence of a vertically non-degenerate closed complex 3-form on Σ×M (see Theorem 4.3 below), which determines a family of J-symplectic structures on (M,J) parametrized by Σ. |
| Keywords: | Cauchy–Riemann forms Hamiltonian formalism J-symplectic manifold |
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