Harmonic morphisms from the classical non-compact semisimple Lie groups

Summary, in English

We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups View the MathML source, SU*(2n) and View the MathML source equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.

• Författare: Sigmundur Gudmundsson; Anna Sakovich
• Avdelning/ar: Matematik (naturvetenskapliga fakulteten); Differential Geometry
• Publiceringsår: 2009
• Språk: Engelska
• Sidor: 47-63
• Publikation/Tidskrift/Serie: Differential Geometry and its Applications
• Volym: 27
• Issue: 1
• Länkar: http://dx.doi.org/10.1016/j.difgeo.2008.10.003
• Dokumenttyp: Artikel i tidskrift
• Förlag: North-Holland
• Ämne: Geometry
• Nyckelord: Harmonic morphisms; Minimal submanifolds; Lie groups
• Status: Published
• Forskningsgrupp: Differential Geometry
• ISBN/ISSN/Övrigt: ISSN: 1872-6984