Submanifold geometry and Morse theory in finite and infinite dimensions
Normal Congruences and Lagrangian submanifolds in spaces of geodesics
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Author(s): |
Total Authors: 2
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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
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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 |