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Japanese journal of mathematics
Article . 2004 . Peer-reviewed
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Maslovian Lagrangian immersions of real space forms into complex space forms

Authors: CHEN, Bang-Yen; GARAY, Oscar J.;

Maslovian Lagrangian immersions of real space forms into complex space forms

Abstract

Consider a Lagrangian immersion, i.e., an immersion of a Riemannian manifold \(M\) into a Kähler \(n\)-manifold \(\overline{M}\) such that it is an isometric immersion whose complex structure \(J\) of \(\overline{M}\) interchanges each tangent space of \(M\) with its corresponding normal space. A Lagrangian immersion is called Masolvian if its Maslov vector field \(JH\), where \(H\) is the mean curvature of \(M\), is a principal direction of the shape operator \(A_H\) of \(M\). The authors classify Maslovian Lagrangian immersions of real space forms of dimension \(\geq 3\) into complex space forms, completing the work of the first author, of \textit{N. Ejiri} [Proc. Am. Math. Soc. 84, 243--246 (1982; Zbl 0485.53022)] and several others. This paper is clearly written.

Keywords

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Local submanifolds, Lagrangian immersions, Global differential geometry of Hermitian and Kählerian manifolds, complex space form, Lagrangian cylinder, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Maslovian Lagrangian immersion, Lagrangian submanifolds; Maslov index, Special Riemannian manifolds (Einstein, Sasakian, etc.), Maslovian immersions, Maslov form, Lagrangian immersion, Lagrangian pseudo-sphere, isometric immersions, real space form

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Top 10%
Top 10%
bronze