Harmonic maps into Lie groups and homogeneous spaces

✍ Scribed by Yu-Jie Dai; Michihiko Shoji; Hajime Urakawa

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 693 KB
• Volume: 7
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(96)00045-9

✦ Synopsis

The tension field of a smooth map of an arbitrary Riemannian manifold into any homogeneous space (G/K, h) with an invariant Riemannian metric h is calculated. As its applications, a characterization of harmonic maps into any homogeneous space is given and all harmonic maps of the standard Euclidean space (R m, go) into a Lie group (G, h) with left invariant Riemannian metric h, of the form f(xl ..... xm) = exp(xl Xl)'" exp(xm Xm) are determined.