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HOLOMORPHIC FOLIATIONS, HARMONIC MORPHISMS AND THE WALCZAK FORMULA

Published online by Cambridge University Press:  17 November 2003

MARTIN SVENSSON
MARTIN SVENSSON
Affiliation:
Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, [email protected]
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Abstract

A formula of Walczak is applied to two situations in differential geometry. Holomorphic distributions on Kähler manifolds are studied, and it is shown how the formula simplifies to a Bochner type formula, which is particularly useful in the study of integrable distributions. Then the Walczak formula is applied in the context of harmonic morphisms, where it provides a means of investigating the vertical Laplacian of the dilation. It is shown that, under some additional conditions on the map and the domain, the $p$-energy is infinite for $p$ sufficiently large.

Keywords

53C1258E20
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 781 - 794
Copyright
The London Mathematical Society 2003

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