Harmonic space and quaternionic manifolds

ar X iv : d g - ga / 9 60 30 13 v 1 2 4 M ar 1 99 6 Harmonic manifolds with some specific volume densities

We show that noncompact simply connected harmonic manifolds with volume density Θ p (r) = sinh n−1 r is isometric to the real hyperbolic space and noncompact simply connected Kähler harmonic manifold with volume density Θ p (r) = sinh 2n−1 r cosh r is isometric to the complex hyperbolic space. A similar result is also proved for Quaternionic Kähler manifolds. Using our methods we get an alterna...

Nonlinear Dirac Operator and Quaternionic Analysis

Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy– Riemann–Fueter equation are established.

On the twistor space of a (co-)CR quaternionic manifold

We characterise, in the setting of the Kodaira–Spencer deformation theory, the twistor spaces of (co-)CR quaternionic manifolds. As an application, we prove that, locally, the leaf space of any nowhere zero quaternionic vector field on a quaternionic manifold is endowed with a natural co-CR quaternionic structure. Also, for any positive integers k and l, with kl even, we obtain the geometric ob...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Harmonic Space Construction of the Quaternionic Taub-NUT metric

We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set of rules. It exhibits SU(2) × U(1) isometry group and depends on two parameters, TaubNUT ‘mass’ and the cosmological constant. We consider several limiting c...