Geometric realizations of generalized algebraic curvature operators

Details Geometric realizations of generalized algebraic curvature operators Geometric realizations of generalized algebraic curvature operators

2008-11-19

arxiv.org/abs/0811.3180v1

Mathematics

Differential Geometry

Scientific paper

10.1063/1.3049619

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.

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