Non-degeneracy of 2-forms and pfaffian

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

Original languageEnglish
Article number280
Issue number2
StatePublished - 1 Feb 2020

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  • Non-degeneracy
  • Pfaffian
  • Symplectic space


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