Taiwanese Journal of Mathematics

CLASSIFICATION OF A FAMILY OF HAMILTONIAN-STATIONARY LAGRANGIAN SUBMANIFOLDS IN COMPLEX HYPERBOLIC 3-SPACE

Bang-Yen Chen

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Abstract

A Lagrangian submanifold in a Kaehler manifold is said to be Hamiltonian-stationary (or simply $H$-stationary) if it is a critical point of the area functional restricted to (compactly supported) Hamiltonian variations. In an earlier paper \cite{cg}, $H$-stationary Lagrangian submanifolds of constant curvature in the complex projective 3-space $CP^3$ with positive relative nullity are classified. In this paper we completely classify $H$-stationary Lagrangian submanifolds of constant curvature in the complex hyperbolic 3-space $CH^3$ with positive relative nullity. As an immediate by-product, several explicit new families of $H$-stationary Lagrangian submanifolds in $CH^3$ are obtained.

Article information

Source
Taiwanese J. Math., Volume 12, Number 5 (2008), 1261-1284.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500574262

Digital Object Identifier
doi:10.11650/twjm/1500574262

Mathematical Reviews number (MathSciNet)
MR2431894

Zentralblatt MATH identifier
1158.53058

Subjects
Primary: 53D12: Lagrangian submanifolds; Maslov index
Secondary: 53C40: Global submanifolds [See also 53B25] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Keywords
Hamiltonian-stationary $H$-stationary Lorentzian complex space form Lagrangian surfaces twisted product decompositions

Citation

Chen, Bang-Yen. CLASSIFICATION OF A FAMILY OF HAMILTONIAN-STATIONARY LAGRANGIAN SUBMANIFOLDS IN COMPLEX HYPERBOLIC 3-SPACE. Taiwanese J. Math. 12 (2008), no. 5, 1261--1284. doi:10.11650/twjm/1500574262. https://projecteuclid.org/euclid.twjm/1500574262


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