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We prove that the Riemannian geometry of almost K\"ahler manifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold.
Foundations of differential geometry. Vol. I
Shoshichi Kobayashi and Katsumi Nomizu · 1963
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Quantum Theory of a Massless Relativistic Surface and a Two-dimensional Bound State Problem
Jens Hoppe · 1982
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Toeplitz quantization of Kähler manifolds and gl ( N ) {\rm gl}(N) , N → ∞ N\to\infty limits
Martin Bordemann, Eckhard Meinrenken, and Martin Schlichenmaier · 1994
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Graph Techniques for Matrix Equations and Eigenvalue Dynamics
Joakim Arnlind · 2008
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Representation theory of C C -algebras for a higher-order class of spheres and tori
Joakim Arnlind · 2008
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Fuzzy Riemann surfaces
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Noncommutative Riemann surfaces by embeddings in ℝ 3 \mathbb{R}^{3}
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Affine transformation crossed product type algebras and noncommutative surfaces
Joakim Arnlind and Sergei Silvestrov · 2009
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J. Arnlind, J. Hoppe, and G. Huisken · 2010
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On the classical geometry of embedded manifolds in terms of Nambu brackets
J. Arnlind, J. Hoppe, and G. Huisken · 2010
Cited alongside, same era.
On the classical geometry of embedded surfaces in terms of Poisson brackets
J. Arnlind, J. Hoppe, and G. Huisken · 2010
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Curvature and Gravity Actions for Matrix Models
Daniel N. Blaschke and Harold Steinacker · 2010
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Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
Daniel N. Blaschke and Harold Steinacker · 2010
Later among the works it cites.
Multi-linear formulation of differential geometry and matrix regularizations
J. Arnlind, J. Hoppe, and G. Huisken · 2012
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