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“A finiteness theorem for Riemannian submersions”

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ANNALES

POLONICI MATHEMATICI LVIII.3 (1993)

Erratum to the paper

“A finiteness theorem for Riemannian submersions”

(Ann. Polon. Math. 57 (1992), 283–290)

by Pawe l G. Walczak ( L´od´z)

In [1], due to the author’s lack of attention, the condition (e) the norm of the integrability tensor A of f ,

A(X, Y ) = h∇

hX

vY + v∇

hX

hY , is bounded by τ ,

is missing in the list of conditions defining the class R(D, V, κ, τ, p, n). With- out it the Theorem is not true, nor is the remark of the introduction saying that the conditions on f imply the geometry (in particular, the curvature) bounds for M . In the proof of the Theorem, condition (e) is involved when applying Lemma 2 to show that the map Ψ has maximal rank.

The author is grateful to Pierre Molino for bringing the lack of some estimates to his attention.

Reference

[1] P. G. W a l c z a k, A finiteness theorem for Riemannian submersions, Ann. Polon.

Math. 57 (1992), 283–290.

INSTITUTE OF MATHEMATICS UNIVERSITY OF L ´OD´Z BANACHA 22

90-238 L ´OD´Z, POLAND

Re¸ cu par la R´ edaction le 25.7.1993

Cytaty

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