Dual Forms of the Squares of Nijenhuis Tensor

TL;DR

This paper explores the dual forms of the squares of the Nijenhuis tensor, expressing them through second order derivatives of the exterior derivative, and presents new conditions under which these squares vanish.

Contribution

It introduces a novel expression for the dual forms of the squares of the Nijenhuis tensor using second order derivatives and establishes new vanishing results.

Findings

Derived new expressions for dual forms of Nijenhuis tensor squares

Established conditions for vanishing of Nijenhuis tensor squares

Enhanced understanding of Nijenhuis tensor properties

Abstract

We express the dual forms of squares of Nijenhuis tensor in terms of the second order component derivatives of the exterior derivative on differential forms and give new vanishing results for the squares of Nijenhuis tensor.