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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This work is partially supported by the Belgian Interuniversity Attraction Pole P07/18 (Dygest) and Project 3E160361 (Lagrangian and calibrated submanifolds) of the KU Leuven Research Fund and was carried out while the first author visited KU Leuven supported by The Scientific and Technological Research Council of Turkey (TUBITAK) Under Grant 1059B141500244.
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Bektaş, B., Van der Veken, J. & Vrancken, L. Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map. Ann Glob Anal Geom 52, 45–55 (2017). https://doi.org/10.1007/s10455-017-9548-2
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DOI: https://doi.org/10.1007/s10455-017-9548-2