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Department of Mathematical Sciences

Staff

Publication details for Dr John Bolton

Bolton, John. & Vrancken, Luc. (2006). Lagrangian submanifolds attaining equality in the improved Chen's inequality. Bulletin of the Belgian Mathematical Society - Simon Stevin 13.
  • Publication type: Journal papers: academic

Author(s) from Durham

Abstract

In \cite{O} Oprea gave an improved version of Chen's inequality for Lagrangian submanifolds of $\mathbb CP^n(4)$. For minimal
submanifolds this inequality coincides with a previous version proved in \cite{CDVV1}. We consider here those non-minimal $3$-dimensional Lagrangian submanifolds in $\mathbb CP^3 (4)$ attaining at all points equality in the improved Chen inequality.
We show how all such submanifolds may be obtained starting from a minimal Lagrangian surface in $\mathbb CP^2(4)$.
% with the aid of some particular curve in $S^3(1)$.