Lagrangian immersions in the product of Lorentzian two manifolds

Autor(es)

Georgiou, Nikos ^{[1, 2]}

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Math & Stat, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Math, BR-13565905 Sao Carlos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Geometriae Dedicata; v. 178, n. 1, p. 1-13, OCT 2015.
• Citações Web of Science: 0

Resumo

For Lorentzian two manifolds and we consider the two product para-Kahler structures defined on the product four manifold , with . We show that the metric is locally conformally flat (resp. Einstein) if and only if the Gauss curvatures of , respectively, are both constants satisfying (resp. ). We give the conditions on the Gauss curvatures for which every Lagrangian surface with parallel mean curvature vector is the product , where and are geodesics. We study Lagrangian surfaces in the product with parallel mean curvature vector and finally, we explore the stability and Hamiltonian stability of certain minimal Lagrangian surfaces and -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