by using the properties of derivatives and the Taylor’s formula we show the existence of analogy of classic tensor analysis. Having a definition of scalar product we define the operation of raising and lowering of indexes.

The next result is the definition a Riemannian tensor on a formal manifold. [*A formal manifold*]{} is a notion of SDG which is represent a classical notion of manifold [@Ko]. It has a number of good and natural properties. It is possible to define a local charts of points which are formal etale subojects of $R^n$, and to show that tangent $T_pM$ space at each point $p$ has the structure of $R$-module and is isomorphic to $R^n$.

Let $M$ be a formal manifold. A map $g:TM\times_M TM\rightarrow R$ is called [*pseudo-Riemannian metric or structure* ]{} on $M$ if the following conditions are satisfied:

1.  $v\# 0 \Rightarrow \exists u: g(v, u)\# 0 $\
    $v=0   \Rightarrow g(v, v)=0 $

2.  $g(v, w)=g(w, v) $

3.  $g(u+v, w)=g(u, w)+g(v, w) $

4.  $g(\lambda \cdot v, w)=\lambda \cdot g (v, w) $

where $\lambda \in R$, $v, w, u \in TM $ so that $v(0)=w(0)=u(0)$.

A map $g_p:T_{p}M\times T_{p}M\rightarrow R $ is a scalar product on $T_{p}M$ 