Harmonic morphisms from the classical non-compact semisimple Lie groups

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We construct the first known complex valued harmonic morphisms from the non-compact Lie groups SL(n,R), SU*(2n) and Sp(n,R) 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.
24 pages

Keywords

Differential Geometry, 58E20, 53C43, 53C12

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/125490

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701520
 http://arxiv.org/abs/math/0701520

Collections

arXiv