• REALIZATIONS OF THREE-DIMENSIONAL GROUP ACTIONS

SIMON DAVIS

Abstract


The minimum dimensions of the real representations of the three-dimensional Lie algebras defining the maximal transitive groups on the basic three-geometries are given. The vector fields on Nil geometry are used to define a differential operator, and the kernel is found. The dynamics of Ricci solitons on this manifold and the embedding in four-dimensions are described.


Keywords


three dimensions, vector fields, Ricci solitons, embedding.

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