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Holomorphic-conformal correspondence in tangent bundles of a Riemannian space. (Russian) Zbl 0568.53012

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.

MSC:

53B20 Local Riemannian geometry
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