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Periodica Mathematica Hungarica

, Volume 44, Issue 1, pp 7–26 | Cite as

Algebraic curvature tensors whose skew-symmetric curvature operator has constant rank 2

  • Peter Gilkey
  • Tan Zhang
Article

Abstract

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature (p,q) where q≥5. If π is a spacelike 2 plane, let R(π) be the associated skew-symmetric curvature operator. We classify the algebraic curvature tensors so R(ċ) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov–Petrova algebraic curvature tensors of rank 2; these are the algebraic curvature tensors of constant rank 2 such that the complex Jordan normal form of R(ċ) is constant.

Keywords

Normal Form Curvature Tensor Curvature Operator Algebraic Curvature Flat Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Peter Gilkey
    • 1
  • Tan Zhang
    • 2
  1. 1.Mathematics DepartmentUniversity of OregonEugeneUSA
  2. 2.Mathematics DepartmentMurray State UniversityMurrayUSA

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