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

Burcu Bektaş Demirci | Zendy; Joeri Van der Veken | Zendy; Luc Vrancken | Zendy

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

Author(s) -

Burcu Bektaş Demirci,

Joeri Van der Veken,

Luc Vrancken

Publication year - 2017

Publication title -

annals of global analysis and geometry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.776

H-Index - 37

eISSN - 1572-9060

pISSN - 0232-704X

DOI - 10.1007/s10455-017-9548-2

Subject(s) - gauss map , mathematics , differential geometry , harmonic map , gauss , codimension , mathematical analysis , type (biology) , harmonic , partial differential equation , surface (topology) , spherical harmonics , pure mathematics , geometry , physics , quantum mechanics , biology , ecology

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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