We use the modified Riemannian extension of an affine surface to construct Bach flat manifolds. As all these examples have vanishing scalar invariants, we shall construct scalar invariants which are not of Weyl type to distinguish them. We illustrate these phenomena in the context of homogeneous affine surfaces.
Constructing Bach flat manifolds of signature (2, 2) using the modified Riemannian extension
E. Calviño-Louzao, E. García-Río, P. Gilkey, I. Gutiérrez-Rodríguez, R. Vázquez-Lorenzo; Constructing Bach flat manifolds of signature (2, 2) using the modified Riemannian extension. J. Math. Phys. 1 January 2019; 60 (1): 013511. https://doi.org/10.1063/1.5080319
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