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Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map

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Type
Preprint
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arXiv ID: 1604.06657
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arXiv
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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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