On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms

Autor(es)

Georgiou, Nikos ^[1] ; Lobos, Guillermo A. ^[2]

Afiliação do(s) autor(es)

^[1] Waterford Inst Technol, Dept Comp & Math, Waterford - Ireland

^[2] Univ Fed Sao Carlos, Dept Math, BR-13560 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ARCHIV DER MATHEMATIK; v. 106, n. 3, p. 285-293, MAR 2016.
• Citações Web of Science: 0

Resumo

We prove that a deformation of a hypersurface in an (n + 1)-dimensional real space form induces a Hamiltonian variation of the normal congruence in the space of oriented geodesics. As an application, we show that every Hamiltonian minimal submanifold in (resp. ) with respect to the (para-)Kahler Einstein structure is locally the normal congruence of a hypersurface in (resp. ) that is a critical point of the functional , where k (i) denote the principal curvatures of and . In addition, for , we prove that every Hamiltonian minimal surface in (resp. ), with respect to the (para-)Kahler conformally flat structure, is the normal congruence of a surface in (resp. ) that is a critical point of the functional (resp. ), where H and K denote, respectively, the mean and Gaussian curvature of . (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