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December 1998 Intrinsic and extrinsic structures of Lagrangian surfaces in complex space forms
Bang-Yen Chen
Tsukuba J. Math. 22(3): 657-680 (December 1998). DOI: 10.21099/tkbjm/1496163671

Abstract

Lagrangian $H$-umbilical submanifolds introduced in $[1, 2]$ can be regarded as the simplest Lagrangian submanifolds in Kaehler manifolds next to totally geodesic ones. It was proved in [1] that Lagrangian $H$-umbilical submanifolds of dimension $\geq 3$ in complex Euclidean spaces are complex extensors, Lagrangian pseudo-spheres, and flat Lagrangian $H$-umbilical submanifolds. Lagrangian $H$-umbilical submanifolds of dimension $\geq 3$ in non-flat complex space forms are classified in [2]. In this paper we deal with the remaining case; namely, non-totally geodesic Lagrangian $H$-umbilical surfaces in complex space forms. Such Lagrangian surfaces are characterized by a very simple property; namely, $JH$ is an eigenvector of the shape operator $A_{H}, where $H$ is the mean curvature vector field. The main operator of this paper is to determine both the intrinsic and the extrinsic structures of Lagrangian $H$-umbilical surfaces.

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Bang-Yen Chen. "Intrinsic and extrinsic structures of Lagrangian surfaces in complex space forms." Tsukuba J. Math. 22 (3) 657 - 680, December 1998. https://doi.org/10.21099/tkbjm/1496163671

Information

Published: December 1998
First available in Project Euclid: 30 May 2017

zbMATH: 0930.53022
MathSciNet: MR1674103
Digital Object Identifier: 10.21099/tkbjm/1496163671

Rights: Copyright © 1998 University of Tsukuba, Institute of Mathematics

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Vol.22 • No. 3 • December 1998
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