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CURVATURE TENSORS WHOSE JACOBI OR SZABÓ OPERATOR IS NILPOTENT ON NULL VECTORS

Published online by Cambridge University Press:  24 March 2003

PETER GILKEY  and
IVA STAVROV
PETER GILKEY
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USAgilkey@darkwing.uoregon.edu
IVA STAVROV
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USAstavrov@hopf.uoregon.edu
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Abstract

The authors show that any $k$ -Osserman Lorentzian algebraic curvature tensor has constant sectional curvature, and give an elementary proof that any local 2-point homogeneous Lorentzian manifold has constant sectional curvature. They also show that a Szabó Lorentzian covariant derivative algebraic curvature tensor vanishes.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 6 , November 2002 , pp. 650 - 658
Copyright
© The London Mathematical Society 2002

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Footnotes

Research partially supported by the NSF (USA) and the MPI (Leipzig).