We construct tame differential calculi coming from toral actions on a class of $\mathrm{C}^*$-algebras. Relying the existence unique Levi-Civita connection such calculus, we prove version Bianchi identity. A Gauss-Bonnet theorem for canonical calculus rank two is studied.

The fundamental ideas of the applicability of Levi-Malcev Theorem for Bol algebras, which plays a basic role in structural theory are outlined

We investigate the accumulation to singular points of leaves of codimension one foliations whose normal bundle is ample, with emphasis on the nonexistence of Levi-flat hypersurfaces.

The starting point of the famous structure theorems on Berwald spaces due to Z.I. Szabó [4] is an observation on the Riemann-metrizability of positive definite Berwald manifolds. It states that there always exists a Riemannian metric on the underlying manifold such that its Levi-Civita connection is just the canonical connection of the Berwald manifold. In this paper we present a new elementary...