Four-dimensional manifolds with degenerate self-dual Weyl curvature operator

被引：5

作者：

Cortes-Ayaso, Alexandre ^{[1
]}

Diaz-Ramos, J. Carlos ^{[2
]}

Garcia-Rio, Eduardo ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Fac Math, Santiago De Compostela 15782, Spain

[2] Natl Univ Ireland Univ Coll Cork, Dept Math, Cork, Ireland

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2008年 / 34卷 / 02期

关键词：

para-Hermitian and para-Kahler structure; self-dual weyl curvature tensor; walker metric;

D O I：

10.1007/s10455-007-9101-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that any four-dimensional Walker metric of nowhere zero scalar curvature has a natural almost para-Hermitian structure. In contrast to the Goldberg-Sachs theorem, if this structure is self-dual and *-Einstein, it is symplectic but not necessarily integrable. This is due to the non-diagonalizability of the self-dual Weyl conformal curvature tensor.

引用

页码：185 / 193

页数：9

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