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The WeitzenbÕck formula for the Bach operator

Published online by Cambridge University Press:  22 January 2016

Mitsuhiro Itoh
Mitsuhiro Itoh*
Affiliation:
Institute of Mathematics, University of Tsukuba 305, Japan
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(Anti-)self-dual metrics are 4-dimensional Riemannian metrics whose Weyl conformai tensor W half vanishes. The Weyl conformai tensor W of an arbitrary metric on an oriented 4-manifold has in general the self-dual part W+ and the anti-self-dual part W− with respect to the Hodge star operator * and one says that a metric is self-dual or anti-self-dual if W− = 0 or W+ = 0, respectively.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 137 , March 1995 , pp. 149 - 181
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

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