| Texto completo | |
| Autor(es): |
Georgiou, Nikos
[1]
Número total de Autores: 1
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| Afiliação do(s) autor(es): | [1] Univ Fed Amazonas, Inst Ciencias Exatas, Manaus, Amazonas - Brazil
Número total de Afiliações: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | TOHOKU MATHEMATICAL JOURNAL; v. 67, n. 1, p. 137-152, MAR 2015. |
| Citações Web of Science: | 0 |
| Resumo | |
Let (Sigma(1), g(1)) and (Sigma(2), g(2)) be connected, complete and orientable 2-dimensional Riemannian manifolds. Consider the two canonical Kahler structures (G(epsilon), J, Omega(epsilon)) on the product 4-manifold Sigma(1) x Sigma(2) given by G(epsilon) = g(1) circle plus g(2), epsilon = +/- 1 and J is the canonical product complex structure. Thus for epsilon = 1 the Kahler metric G(+) is Riemannian while for epsilon = -1, G(-) is of neutral signature. We show that the metric G(epsilon) is locally conformally flat if and only if the Gauss curvatures kappa(g(1)) and kappa(g(2)) are both constants satisfying kappa(g(1)) = -epsilon kappa(g(2)). We also give conditions on the Gauss curvatures for which every G(epsilon)-minimal Lagrangian surface is the product gamma(1) x gamma(2) subset of Sigma(1) x Sigma(2), where gamma(1) and gamma(2) are geodesics of (Sigma(1), g(1)) and (Sigma(2), g(2)), respectively. Finally, we explore the Hamiltonian stability of projected rank one Hamiltonian G(epsilon)-minimal surfaces. (AU) | |
| Processo FAPESP: | 10/08669-9 - Congruências normais e subvariedades lagrangeanas nos espaços de geodésicas |
| Beneficiário: | Nikos Georgiou |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |