On Hamiltonian minimal submanifolds in the space o... - BV FAPESP
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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Georgiou, Nikos [1] ; Lobos, Guillermo A. [2]
Total Authors: 2
Affiliation:
[1] Waterford Inst Technol, Dept Comp & Math, Waterford - Ireland
[2] Univ Fed Sao Carlos, Dept Math, BR-13560 Sao Carlos, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: ARCHIV DER MATHEMATIK; v. 106, n. 3, p. 285-293, MAR 2016.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 10/08669-9 - Normal Congruences and Lagrangian submanifolds in spaces of geodesics
Grantee:Nikos Georgiou
Support Opportunities: Scholarships in Brazil - Post-Doctoral