Biharmonic Lagrangian submanifolds in K\"ahler manifolds
Shun Maeta, Hajime Urakawa
TL;DR
This paper establishes conditions for biharmonic Lagrangian submanifolds in Kähler manifolds and classifies specific biharmonic submanifolds in complex space forms, advancing understanding in differential geometry.
Contribution
It provides necessary and sufficient conditions for biharmonicity and classifies biharmonic PNMC Lagrangian submanifolds in complex space forms, a novel classification result.
Findings
Characterization of biharmonic Lagrangian submanifolds in Kähler manifolds
Classification of biharmonic PNMC Lagrangian submanifolds in complex space forms
Conditions linking biharmonicity to geometric properties
Abstract
We give necessary and sufficient conditions for a Lagrangian submanifold of a K\"ahler manifold to be biharmonic. Furthermore, we classify biharmonic PNMC Lagrangian submanifolds in the complex space forms.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology