Invariant forms, associated bundles and Calabi-Yau metrics (Q2475447)

In this paper, the author develops a method, initially introduced by Salomon in [\textit{R. Bryant, S. Salamon}, Duke Math. J. 58, 829--850 (1989; Zbl 0681.53021)] and [\textit{S. Salamon}, Riemannian geometry and holonomy groups. Harlow: Longman Scientific \& Technical; New York: John Wiley \& Sons (1989; Zbl 0685.53001)], for computing the space of invariant forms on an associated bundle \(X=P\times_G V\), associated with a generic \(G\)-structure \(P\). Not assuming that the base manifold \(P/G\) is a homogeneous space, he presents a definition of invariance for forms on \(X\) that generalizes the notion of \(H\)-invariant forms in the homogeneous case. As an application of his method, the author computes the space of invariant forms on \(T\mathbb CP^2\), and obtains a two-parameter family of local Calabi-Yau metrics with conical Kähler form, generalizing the known conical hyper-Kähler example.