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A Kähler Compatible Moyal Deformation of the First Heavenly Equation
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a noncommutative Kähler manifold based on a non-linear perturbations of Moyal integrable deformations of $D=4$ self-dual gravity. The deformed Kähler manifold preserves all the properties of the commutative one, and we obtain the associated noncommutative Kähler potential using the Moyal deformed gravity approach. We apply this construction to the Atiyah–Hitchin metric and its Kähler potential, which is useful in the description of interactions among magnetic monopoles at low energies.
Keywords: heavenly equations, Moyal deformation, Atiyah–Hitchin metric. 
@article{SIGMA_2019_15_a72,
     author = {Marco Maceda and Daniel Mart{\'\i}nez-Carbajal},
     title = {A {K\"ahler} {Compatible} {Moyal} {Deformation} of the {First} {Heavenly} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
     volume = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a72/}
}
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Marco Maceda; Daniel Martínez-Carbajal. A Kähler Compatible Moyal Deformation of the First Heavenly Equation. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a72/

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