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October, 2002 Classification of flat slant surfaces in complex Euclidean plane
Bang-Yen CHEN
J. Math. Soc. Japan 54(4): 719-746 (October, 2002). DOI: 10.2969/jmsj/1191591991


It is well-known that the classification of flat surfaces in Euclidean 3space is one of the most basic results in differential geometry. For surfaces in the complex Euclidean plane C2 endowed with almost complex structure J, flat surfaces are the simplest ones from intrinsic point of views. On the other hand, from J-action point of views, the most natural surfaces in C2 are slant surfaces, i.e., surfaces with constant Wintinger angle. In this paper the author completely classifies flat slant surfaces in C2. The main result states that, beside the totally geodesic ones, there are five large classes of flat slant surfaces in C2. Conversely, every non-totally geodesic flat slant surfaces in C2 is locally a surface given by these five classes.


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Bang-Yen CHEN. "Classification of flat slant surfaces in complex Euclidean plane." J. Math. Soc. Japan 54 (4) 719 - 746, October, 2002.


Published: October, 2002
First available in Project Euclid: 5 October 2007

zbMATH: 1038.53054
MathSciNet: MR1921086
Digital Object Identifier: 10.2969/jmsj/1191591991

Primary: 53C40 , 53C42
Secondary: 53A05

Keywords: complex Euclidean space , flat surface , slant submanifold , slant surface , wave equation

Rights: Copyright © 2002 Mathematical Society of Japan


Vol.54 • No. 4 • October, 2002
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