Explicit Classification of Parallel Lorentz Surfaces in 4D Indefinite Space Forms With Index 3
Vol. 5 No. 3 (2010) P.311~P.348
A Lorentz surface in an indefinite space form is called parallel if its second fundamental
form is parallel. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel
surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Parallel Lorentz surfaces in 4D Lorentzian space
forms are classified in  by Chen and Van der Veken. Moreover, explicit classification of parallel Lorentz surfaces in 4D indefinite space forms with index 2 are obtained recently in a series of papers by Chen, Dillen and Van der Veken [12, 13, 14].
In this paper, we obtain the complete classification of parallel
Lorentz surfaces in 4D indefinite space forms with index 3. Consequently, the complete classification of parallel Lorentz
surfaces in 4D indefinite space forms are achieved.
Lorentz surface, parallel surface, indenite space form, pseudo 4-sphere, pseudo-hyperbolic space
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 53C42, 81Q70, 53C50
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Revised : 2010-04-05