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J. Korean Math. Soc. 2015; 52(3): 523-535
Printed May 1, 2015
https://doi.org/10.4134/JKMS.2015.52.3.523
Copyright © The Korean Mathematical Society.
Translation and homothetical surfaces in Euclidean space with constant curvature
Rafael L\'opez and Marilena Moruz
Universidad de Granada, Al. I. Cuza University of Iasi
We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.
Keywords: translation surface, homothetical surface, mean curvature, Gauss curvature
MSC numbers: 53A10, 53C45
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