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}
}