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

Georgiou, Nikos and Lobos, Guillermo A. (2016) On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms. Archiv der Mathematik, 106 (3). pp. 285-293. ISSN 0003-889X

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Abstract

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

Item Type:	Article
Additional Information:	Funding Information: The authors would like to thank Henri Anciaux and Martin A. Magid for their helpful and valuable suggestions and comments. Nikos Georgiou is partially supported by Fapesp? Sao Paulo Research Foundation (2010/08669-9). Publisher Copyright: © 2016, Springer International Publishing.
Uncontrolled Keywords:	/dk/atira/pure/subjectarea/asjc/2600
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Depositing User:	Admin SSL
Date Deposited:	19 Oct 2022 23:09
Last Modified:	07 Jun 2023 18:45
URI:	http://repository-testing.wit.ie/id/eprint/4419

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