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Conformally flat,minimal, Lagrangian submanifolds in complex space forms
Authors:Antić  Miroslava  Vrancken  Luc
Institution:1.Faculty of Mathematics, University of Belgrade, Belgrade, 11000, Serbia
;2.Laboratoire de Mathématiques pour l’Ingénieur, Université Polytechnique Hauts-de-France, Valenciennes, 59313, France
;3.Departement Wiskunde, Katholieke Universiteit Leuven, Leuven, 3001, Belgium
;
Abstract:

We investigate n-dimensional (n ⩾ 4), conformally flat, minimal, Lagrangian submanifolds of the n-dimensional complex space form in terms of the multiplicities of the eigenvalues of the Schouten tensor and classify those that admit at most one eigenvalue of multiplicity one. In the case where the ambient space is ℂn, the quasi umbilical case was studied in Blair (2007). However, the classification there is not complete and several examples are missing. Here, we complete (and extend) the classification and we also deal with the case where the ambient complex space form has non-vanishing holomorphic sectional curvature.

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