Diffeomorphisms conformal on distributions

• Autorzy: Kamil Niedziałomski
• Języki publikacji: EN

Abstrakty

EN

Let f:M → N be a local diffeomorphism between Riemannian manifolds. We define the eigenvalues of f to be the eigenvalues of the self-adjoint, positive definite operator df*df:TM → TM, where df* denotes the operator adjoint to df. We show that if f is conformal on a distribution D, then $dim V_{λ} ≥ 2dim D - dim M$, where $V_{λ}$ denotes the eigenspace corresponding to the coefficient of conformality λ of f. Moreover, if f has distinct eigenvalues, then there is locally a distribution D such that f is conformal on D if and only if 2dim D < dim M + 1.

Kategorie tematyczne

• 53B20: Local Riemannian geometry
• 53A30: Conformal differential geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2009
• Tom: 95
• Numer: 2
• Strony: 115-124

Daty

wydano

2009

Twórcy

autor

Kamil Niedziałomski

• Department of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/ap95-2-2