TITLE

Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane

AUTHOR(S)
Chen, Bang-Yen; Fastenakels, Johan
PUB. DATE
December 2007
SOURCE
Acta Mathematica Sinica;Dec2007, Vol. 23 Issue 12, p2111
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
One of the most fundamental problems in the study of Lagrangian submanifolds from Riemannian geometric point of view is to classify Lagrangian immersions of real space forms into complex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces in the Lorentzian complex plane $$ {\text{\bf {C}}}^{2}_{1} $$ . Our main result states that there are thirty-eight families of flat Lagrangian surfaces in $$ {\text{\bf {C}}}^{2}_{1} $$ . Conversely, every flat Lagrangian surface in $$ {\text{\bf {C}}}^{2}_{1} $$ is locally congruent to one of the thirty-eight families.
ACCESSION #
27500245

 

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