General Relativity and John Archibald Wheeler by Ignazio Ciufolini & Richard A. Matzner

Author:Ignazio Ciufolini & Richard A. Matzner
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

Of course, the ζ-Laplaceequation reduces for ζ2 = − 1 to the ordinary Laplace equation, while for ζ2 = 1 to the wave equation. The operator − ζ2 ∂ x 2 + ∂ y 2 will be called the ζ-Laplace operator.

In the following a ζ-complex structure on will denote an endomorphism of the module of all vector fields on , with J 2 = ζ2 I, J≠0, I, and vanishing Nijenhuis torsion, i.e., J, J FN = 0, where ⋅, ⋅ FN denotes for the Frölicher–Nijenhuis bracket. A 2-dimensional manifold supplied with a ζ-complex structure is called a ζ-complex curve.

Obviously, for ζ2 = − 1 a ζ-complex curve is just an ordinary 1 − dimensional complex manifold (curve).

By using the endomorphism J the ζ-Laplace equation can be written intrinsicallyas

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.