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Article

Существенные группы изометрий некомпактных двумерных плоских лоренцевых орбифолдов

Боголепова Е. В., Жукова Н. И.

Using the bundle of pseudo-orthogonal frames some canonical covering map for two-dimensional Lorentzian orbifolds is constructed and applied. The existence of such map shows that any two-dimensional Lorentzian orbifold is very good.

It is proved that there are only two (up to isomorphisms in the category of orbifolds) two-dimensional smooth noncompact orbifolds admitting complete flat Lorentzian metrics with an essential isometry group. They are the plane and the Z2 -cone. Unlike compact orbifolds, the metric can be any from the class of flat complete Lorentzian metrics. Examples are constructed.