Non-Degeneracy of 2-Forms and Pfaffian

Abstract

In this article, we study the non-degeneracy of 2-forms (skew symmetric (0,2)-tensor) alpha along the Pfaffian of alpha. We consider a symplectic vector space Vwith a non-degenerate skew symmetric (0,2)-tensor omega, and derive various properties of the Pfaffian of alpha. As an application we show the non-degenerate skew symmetric (0,2)-tensor omega has a property of rigidity that it is determined by its exterior power.