Diffeomorphisms conformal on distributions

Kamil Niedziałomski. "Diffeomorphisms conformal on distributions." Annales Polonici Mathematici 95.2 (2009): 115-124. <http://eudml.org/doc/280230>.

@article{KamilNiedziałomski2009,
abstract = {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.},
author = {Kamil Niedziałomski},
journal = {Annales Polonici Mathematici},
keywords = {conformal mappings; distributions; Riemannian manifolds},
language = {eng},
number = {2},
pages = {115-124},
title = {Diffeomorphisms conformal on distributions},
url = {http://eudml.org/doc/280230},
volume = {95},
year = {2009},
}

TY - JOUR
AU - Kamil Niedziałomski
TI - Diffeomorphisms conformal on distributions
JO - Annales Polonici Mathematici
PY - 2009
VL - 95
IS - 2
SP - 115
EP - 124
AB - 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.
LA - eng
KW - conformal mappings; distributions; Riemannian manifolds
UR - http://eudml.org/doc/280230
ER -