Classification of Casorati ideal Lagrangian submanifolds in complex space forms

By Mohd. Aquib, Jae Won Lee, Gabriel Eduard Vîlcu, D. Yoon. Differential geometry and its applications, 2019

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Abstract In this paper, using optimization methods on Riemannian submanifolds, we establish two improved inequalities for generalized normalized δ-Casorati curvatures of Lagrangian submanifolds in complex space forms. We provide examples showing that these inequalities are the best possible and classify all Casorati ideal Lagrangian submanifolds (in the sense of B.-Y. Chen) in a complex space form. In particular, we generalize the recent results obtained in G.E. Vilcu (2018) [34] .

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/48fbf0d049018ad57f16e8fabe3d206eaa44ad67