Abstract
In this article, we study Codazzi couplings of an arbitrary connection ∇ with a a nondegenerate
2-form !, an isomorphism L on the space of derivation of rho-commutative algebra A, which the
important examples of isomorphism L are almost complex and almost para-complex structures, a metric
g that (g; !;L) form a compatible triple. We study a statistical structure on rho-commutative algebras by
the classical manner on Riemannian manifolds. Then by recalling the notions of almost (para-)Kähler
rho-commutative algebras, we generalized the notion of Codazzi-(para-)Kähler rho-commutative algebra as
a (para-)Kähler (or Fedosov) rho-commutative algebra which is at the same time statistical and moreover
define the holomorphic rho-commutative algebras.
Subject
Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis
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