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Paracomplex projective models and harmonic maps into them. (English) Zbl 0957.53036

Paracomplex projective models are para-Kähler space forms (and models of constant paraholomorphic sectional curvature of dimension greater than 2) introduced by P. M. Gadea and A. Montesinos Amilibia [Pac. J. Math. 136, 85-101 (1989; Zbl 0706.53024)]. These models are considered with their usual para-Kähler structure. The author introduces two different extra structures, so that \((\mathbb{P}_m (\mathbb{A}),J,g)\) becomes a para-Kähler space form and \((\mathbb{P}_m(\mathbb{A}), P,G^c)\) becomes an almost para-Kähler manifold. Then, the harmonicity of maps into the two given types of manifolds is discussed and some harmonic maps are constructed from certain paraholomorphic ones.

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
58E20 Harmonic maps, etc.
53C43 Differential geometric aspects of harmonic maps
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)

Citations:

Zbl 0706.53024
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