Kapustina, T. V. Holomorphic-conformal correspondence in tangent bundles of a Riemannian space. (Russian) Zbl 0568.53012 Tr. Geom. Semin. 13, 39-48 (1981). For a Riemannian metric of a manifold \(V_ n\), a metric, called a ”synectic metric”, is locally defined in \(T(V_ n)\) (the manifold of tangent vectors to \(V_ n)\) or in \(T_ 2(V_ n)\). For two such metrics a correspondence called holomorphic-conformal correspondence is defined. A holomorphic-conformal Euclidean metric is a synectic metric holomorphic-conformal to the lift of a Euclidean metric of \(V_ n\). The symmetric holomorphic-conformal Euclidean metrics are determined. Cited in 1 Document MSC: 53B20 Local Riemannian geometry Keywords:holomorphic-conformal correspondence; synectic metric PDFBibTeX XMLCite \textit{T. V. Kapustina}, Tr. Geom. Semin. 13, 39--48 (1981; Zbl 0568.53012) Full Text: EuDML