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 , where 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-2,
author = {Kamil Niedzia\l omski},
title = {Diffeomorphisms conformal on distributions},
journal = {Annales Polonici Mathematici},
volume = {95},
year = {2009},
pages = {115-124},
zbl = {1162.53011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-2}
}
Kamil Niedziałomski. Diffeomorphisms conformal on distributions. Annales Polonici Mathematici, Tome 95 (2009) pp. 115-124. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-2/