$L^2$-estimates for the $d$-operator acting on super forms

Abstract

In the setting of super forms developed in a previous article by the author, we introduce the notion of $\mathbb{R}$-Kähler metrics on ${\mathbb{R}}^n$. We consider existence theorems and $L^2-$estimates for the equation $d\alpha =\beta$, where $\alpha$ and $\beta$ are super forms, in the spirit of Hörmander's $L^2-$estimates for the $\bar{\partial }-$equation on a complex Kähler manifold.

22 pages