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      Classification of \(\delta(2,n-2)\)-ideal Lagrangian submanifolds in \(n\)-dimensional complex space forms

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          Abstract

          It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold \(M\) of a complex space form \(\tilde M^{n}(4c)\) of constant holomorphic sectional curvature \(4c\) satisfies the following optimal inequality: \begin{align*} \delta(2,n-2) \leq \frac{n^2(n-2)}{4(n-1)} H^2 + 2(n-2) c, \end{align*} where \(H^2\) is the squared mean curvature and \(\delta(2,n-2)\) is a \(\delta\)-invariant on \(M\). In this paper we classify Lagrangian submanifolds of complex space forms \(\tilde M^{n}(4c)\), \(n \geq 5\), which satisfy the equality case of this inequality at every point.

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          Most cited references 11

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          Some pinching and classification theorems for minimal submanifolds

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              Interaction of Legendre curves and Lagrangian submanifolds

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                Author and article information

                Journal
                2017-05-01
                Article
                1705.00685

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                53D12, 53C40
                26 pages
                math.DG

                Geometry & Topology

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