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- W2894103208 abstract "We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the 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 seven types of invariant surfaces, which then generalizes the study of revolution and helicoidal surfaces in Euclidean and Lorentzian spaces to the context of singular metrics. After computing the two fundamental forms of these surfaces and their Gaussian and mean curvatures, we solve the corresponding problem of prescribed curvature for invariant surfaces whose generating curves lie on a plane containing the degenerated direction." @default.
- W2894103208 created "2018-10-05" @default.
- W2894103208 creator A5012413487 @default.
- W2894103208 date "2018-09-28" @default.
- W2894103208 modified "2023-10-16" @default.
- W2894103208 title "Differential geometry of invariant surfaces in simply isotropic and pseudo-isotropic spaces" @default.
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- W2894103208 doi "https://doi.org/10.18926/mjou/60864" @default.
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