Elasticity and conformal tension via the Kaluza–Klein mechanism
نویسندگان
چکیده
The principle of symmetric criticality allows one to reduce the search of symmetric critical points for the conformal total tension functional in a Kaluza–Klein conformal universe, to the search of closed curves in its gravitatory component which are critical points for certain r-elastic energy functionals. The constancy of the mean curvature is preserved in this reduction of symmetry. In this framework we study the r-elasticity of fibres in a semi-Riemannian warped tube. We obtain a wide class of tubes which are foliated by r-elastic circles and give some applications including a characterization of the photon sphere in a Schwarzschild spacetime from the point of view of the r-elasticity. © 2000 Elsevier Science B.V. All rights reserved. MSC: 53C40; 53C50 PACS: 02.40.Ky; 04.65.+e; 11.10.Kk
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