Tohoku Mathematical Journal
2009
March
SECOND SERIES VOL. 61, NO. 1

Tohoku Math. J.
61 (2009), 1-40

Title COMPLETE CLASSIFICATION OF PARALLEL SURFACES IN 4-DIMENSIONAL LORENTZIAN SPACE FORMS

Author Bang-Yen Chen and Joeri Van der Veken

(Received November 19, 2007, revised June 13, 2008)
Abstract. In this paper we completely classify parallel non-degenerate surfaces in 4-dimensional Lorentzian space forms. In addition, we also completely classify non-degenerate surfaces with parallel mean curvature vector in 4-dimensional Lorentzian space forms.

2000 Mathematics Subject Classification. Primary 53B25; Secondary 53C50, 83C15.
Key words and phrases. Lorentzian space form, parallel second fundamental form, surface with parallel mean curvature vector, parallel surface.

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