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Diffeomorphisms conformal on distributions

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Niedziałomski K.

Annales Polonici Mathematici

2009

tom 95

nr 2

115-124

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.

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1 Annales Polonici Mathematici

1 Niedziałomski K.

1 2009

Wyniki wyszukiwania

Diffeomorphisms conformal on distributions