WILLMORE TORI AND WILLMORE-CHEN SUBMANIFOLDS IN PSEUDO-RIEMANNIAN SPACES

We exhibit a new method to find Willmore tori and Willmore-Chen subman ifolds in spaces endowed with pseudo-Riemannian warped product metrics , whose fibres are homogeneous spaces. The chief points are the invari ance of the involved variational problems with respect to the conforma l changes of the metrics on the ambient spaces and the principle of sy mmetric criticality. They allow us to relate the variational problems with that of generalized elastic curves in the conformal structure of the base space. Among other applications we get a rational one-paramet er family of Willmore tori in the standard anti De Sitter 3-space shap ed on an associated family of closed free elastic curves in the once p unctured standard 2-sphere. We also obtain rational one parameter fami lies of Willmore-Chen submanifolds in standard pseudo-hyperbolic space s. As an application of a general approach to our method, we give nice examples of pseudo-Riemannian 3-spaces which are foliated with leaves being non-trivial Willmore tori. More precisely, the leaves of this f oliation are Willmore tori which are conformal to non-zero constant me an curvature flat tori. (C) 1998 Elsevier Science B.V. All rights rese rved.