Invariant surfaces in homogenous space Sol with constant curvature

Details Invariant surfaces in homogenous space Sol with constant curvature Invariant surfaces in homogenous space Sol with constant curvature

2009-09-14

arxiv.org/abs/0909.2550v1

Mathematics

Differential Geometry

16 pages, 3 figures

Scientific paper

A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curvature. Also, we characterize invariant surfaces that satisfy a linear Weingarten relation.

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