The Square of Nijenhuis Tensor and Its Vanishing Results

TL;DR

This paper explores the properties of the square of the Nijenhuis tensor, providing strong and weak formulations and establishing conditions under which it vanishes, contributing to the understanding of complex geometric structures.

Contribution

It introduces new formulations of the square of the Nijenhuis tensor and presents novel vanishing results, advancing the theoretical understanding of geometric structures.

Findings

Strong and weak forms of the square of Nijenhuis tensor defined

Vanishing conditions for the square established

Enhanced understanding of geometric structures related to Nijenhuis tensor

Abstract

We give the strong form and the weak form of the square of Nijenhuis tensor, and some vanish results of the square.