Hodge type decomposition

• Autorzy: Wojciech Kozłowski
• Języki publikacji: EN

Abstrakty

EN

In the space $Λ^p$ of polynomial p-forms in ℝⁿ we introduce some special inner product. Let $H^p$ be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that $Λ^p$ splits as the direct sum $d*(Λ^{p+1}) ⊕ δ*(Λ^{p-1}) ⊕ H^p$, where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.

Kategorie tematyczne

• 53C43: Differential geometric aspects of harmonic maps
• 35J99: None of the above, but in this section
• 33C55: Spherical harmonics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 90
• Numer: 2
• Strony: 99-104

Daty

wydano

2007

Twórcy

autor

Wojciech Kozłowski

• Institute of Mathematics, Polish Academy of Sciences, Łódź Branch
• Faculty of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/ap90-2-1