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Characterizing warped-product Lagrangian immersions in complex projective space

Part of: Local differential geometry

Published online by Cambridge University Press:  28 May 2009

J. Bolton ,
C. Rodriguez Montealegre  and
L. Vrancken
J. Bolton
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK; Email: ([email protected])
C. Rodriguez Montealegre
Affiliation:
Departamento de Matematicas, Escuela Politécnica Superior, Universidad de Jaen, 23071 Jaen, Spain; Email: ([email protected])
L. Vrancken
Affiliation:
LAMAV, ISTV2, Université de Valenciennes, Campus du Mont Houy, 59313 Valenciennes Cedex 9, France; Email: ([email protected])
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Abstract

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Starting from two Lagrangian immersions and a horizontal curve in S3(1), it is possible to construct a new Lagrangian immersion, which we call a warped-product Lagrangian immersion. In this paper, we find two characterizations of warped-product Lagrangian immersions. We also investigate Lagrangian submanifolds which attain at every point equality in the improved version of Chen's inequality for Lagrangian submanifolds of ℂPn(4) as discovered by Opreaffi We show that, for n≥4, an n-dimensional Lagrangian submanifold in ℂPn(4) for which equality is attained at all points is necessarily minimal.

Keywords

Lagrangian submanifoldcomplex projective spaceChen's δ invariant

MSC classification

Secondary: 53B25: Local submanifolds 53B20: Local Riemannian geometry
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 273 - 286
Copyright
Copyright © Edinburgh Mathematical Society 2009