(Para-) Kähler Structures on $$\rho $$ ρ -Commutative Algebras

Abstract

Recently, geometrics objects such as $$\rho $$ -forms, metrics, Levi–Civita connection, differential calculus were introduced on $$\rho $$ -commutative algebras. In this paper, we intend to extend another geometric objects such as almost complex structure, almost para-complex structure, Hermitian metric, para-Hermitian metric, Kahler and para-Kahler forms, on it and introduce new concepts which we will call Kahler $$\rho $$ -commutative algebras and para-Kahler $$\rho $$ -commutative algebras.