The classification of simple Jacobi–Ricci commuting algebraic curvature tensors


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).

DOI Code: 10.1285/i15900932v28n1supplp341

Keywords: algebraic curvature tensor; Jacobi operator; Ricci operator

Classification: 53C20

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