Abstract

HULETT, Eduardo. On the geometry of a class of conformal harmonic maps of surfaces into . Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.2, pp.23-38. ISSN 0041-6932.

This paper deals with certain advances in the understanding of the geometry of superconformal harmonic maps of Riemann surfaces into De Sitter space . The character of these notes is mainly expository and we made no attempt to provide complete proofs of the main results, which can be found in reference [12]. Our main analytic tool to study superconformal harmonic maps is a Gram-Schmidt algorithm to produce adapted frames for such maps. This allows us to compute the normal curvatures and obtain identities which are used to study their geometry. Some global properties such as fullness and rigidity are considered and a highest order Gauss transform or polar map is constructed and its main properties are discussed.

Keywords : De Sitter space-time; superconformal harmonic maps; harmonic sequences.

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