Article ID Journal Published Year Pages File Type
4617844 Journal of Mathematical Analysis and Applications 2012 14 Pages PDF
Abstract

Lagrangian submanifolds appear naturally in the context of classical mechanics. Moreover, they play some important roles in supersymmetric field theories as well as in string theory. Recently, it was proved in Chen and Dillen (2011) [11] that for any Lagrangian submanifold M   of a complex space form M˜n(4c), n⩾3n⩾3, of constant holomorphic sectional curvature 4c we haveδ(n−1)⩽n−14(nH2+4c), where H2H2 is the squared mean curvature and δ(n−1)δ(n−1) is a δ-invariant of M (cf. Chen, 2000, 2011 [7] and [10]). In this paper, we completely classify non-minimal Lagrangian submanifolds of complex space forms M˜n(4c), c=0,1,−1c=0,1,−1, which satisfy the equality case of the inequality identically.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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