Constructing Bach Flat Manifolds of signature $(2,2)$ using the modified Riemannian extension

E. Calvi\~no-Louzao; E. Garc\'ia-R\'io; I. Guti\'errez-Rodr\'iguez; P. Gilkey; R. V\'azquez-Lorenzo

arxiv: 1807.09218 · v1 · pith:OPSAYK5Bnew · submitted 2018-07-24 · 🧮 math.DG

Constructing Bach Flat Manifolds of signature (2,2) using the modified Riemannian extension

E. Calvi\~no-Louzao , E. Garc\'ia-R\'io , P. Gilkey , I. Guti\'errez-Rodr\'iguez , R. V\'azquez-Lorenzo This is my paper

classification 🧮 math.DG

keywords affinebachconstructextensionflatinvariantsmanifoldsmodified

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We use the modified Riemannian extension of an affine surface to construct Bach flat manifolds. As all these examples are VSI (vanishing scalar invariants), we shall construct scalar invariants which are not of Weyl type to distinguish them. We illustrate this phenomena in the context of homogeneous affine surfaces.

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Constructing Bach Flat Manifolds of signature (2,2) using the modified Riemannian extension

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