engleski

3D homogeneous geometries and some special surfaces

In this lecture we will briefly describe each of the eight homogeneous geometries considering their basic properties. We will devote special attention to understanding of isometry groups of these geometries and discuss homogeneous geometries in light of Cayley's famous phrase "projective geometry is all geometry." The lecture will also outline few important examples of surfaces in twisted product homogeneous geometries (SL(2, R)~, Nil, Sol) e.g. minimal surfaces, CMC surfaces, parallel surfaces etc.

homogeneous geometry; isometry group; minimal surface

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