English

Geometric realizations of generalized algebraic curvature operators

Differential Geometry 2009-11-13 v1

Abstract

We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic curvature is not geometrically realizable by a projectively flat Ricci antisymmetric torsion free connection.

Cite

@article{arxiv.0811.3180,
  title  = {Geometric realizations of generalized algebraic curvature operators},
  author = {P. Gilkey and S. Nikcevic and D. Westerman},
  journal= {arXiv preprint arXiv:0811.3180},
  year   = {2009}
}
R2 v1 2026-06-21T11:43:23.958Z