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Mathematics > Differential Geometry

arXiv:0710.2080 (math)
[Submitted on 10 Oct 2007]

Title:The classification of simple Jacobi--Ricci commuting algebraic curvature tensors

Authors:P. Gilkey, S. Nikcevic
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Abstract: We classify algebraic curvature tensors such that the Ricci operator is simple (i.e. the Ricci operator is complex diagonalizable and either the complex spectrum consists of a single real eigenvalue or the complex spectrum consists of a pair of eigenvalues which are complex conjugates of each other) and which are Jacobi--Ricci commuting (i.e. the Ricci operator commutes with the Jacobi operator of any vector).
Subjects: Differential Geometry (math.DG)
MSC classes: 53C20
Cite as: arXiv:0710.2080 [math.DG]
  (or arXiv:0710.2080v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.2080

Submission history

From: Peter B. Gilkey [view email]
[v1] Wed, 10 Oct 2007 17:55:27 UTC (7 KB)
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