The classification of simple Jacobi–Ricci commuting algebraic curvature tensors

Authors

  • P. Gilkey
  • S. Nikcevic

DOI:

https://doi.org/10.1285/i15900932v28n1supplp341

Keywords:

algebraic curvature tensor, Jacobi operator, Ricci operator

Abstract

We classify algebraic curvature tensors such that the Ricci operator ρ is simple (i.e. ρis complex diagonalizable and Spec{ρ}={a} or Spec{ρ}={a1±a2√-1}) and which are Jacobi–Ricci commuting (i.e. ρJ(v)=J(v)ρ for all v).

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Published

01-10-2008

Issue

Volume 28, suppl. 1 (2008)

Section

Articoli

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode