# Differential geometry of invariant surfaces in simply isotropic and pseudo-isotropic spaces

@article{Silva2018DifferentialGO, title={Differential geometry of invariant surfaces in simply isotropic and pseudo-isotropic spaces}, author={Luiz C. da Silva}, journal={arXiv: Differential Geometry}, year={2018} }

We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of index zero and one, respectively. We show that the one-parameter subgroups of isotropic rigid motions lead to 7 types of invariant surfaces, which then generalizes the study of revolution/helicoidal surfaces in Euclidean and Lorentzian geometries to the context… Expand

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