Geometric realizations of generalized algebraic curvature operators
classification
🧮 math.DG
keywords
algebraiccurvaturegeneralizedantisymmetricflatgeometricprojectivelyricci
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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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