Harmonic vector fields on pseudo-Riemannian manifolds

2015/01/07 by Friswell, R. M., Wood, C. M.
#53C07 #53C20 #53C43 #53C50 #58E20 #58E30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.01622

Abstract

The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields on pseudo-Riemannian quadrics. A para-Kaehler twisted anti-isometry is used to correlate harmonic vector fields on the quadrics of neutral signature.

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