Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map |
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| Authors: | Burcu Bektaş Joeri Van der Veken Luc Vrancken |
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| Affiliation: | 1.Department of Mathematics, Faculty of Science and Letters,Istanbul Technical University,Maslak, Istanbul,Turkey;2.Department of Mathematics,KU Leuven,Leuven,Belgium;3.LAMAV, ISTV2,Université de Valenciennes,Valenciennes Cedex 9,France |
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| Abstract: | We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification is obtained, while in other cases the solutions are described by an explicit system of partial differential equations. |
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