Riemannian geometry on Hom$\rho$commutative algebras
Abstract
Recently, some concepts such as Homalgebras, HomLie algebras, HomLie admissible algebras, Homcoalgebras are studied and some of classical properties of algebras and some geometric objects are extended on them. In this paper by recall the concept of Hom$\rho$commutative algebras, we intend to develop some of the most classical results in Riemannian geometry such as metric, connection, torsion tensor, curvature tensor on it and also we discuss about differential operators and get some results of differential calculus using them. The notions of symplectic structures and Poisson structures are included and an example of $\rho$Poisson bracket is given.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1810.13298
 Bibcode:
 2018arXiv181013298B
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Rings and Algebras
 EPrint:
 18 pages