Apanasov, Boris N. Kobayashi conformal metric on manifolds, Chern-Simons and \(\eta\)- invariants. (English) Zbl 0761.53010 Int. J. Math. 2, No. 4, 361-382 (1991). A canonical Riemannian smooth metric is constructed on a given uniformized conformal manifold (conformally flat manifold), a metric compatible with the conformal structure. The Kobayashi approach for the construction of a biholomorphically invariant intrinsic pseudo-metric in a complex analytic space is carried over to the conformal (Moebius) category. Infinitesimal and regularity properties for this Kobayashi conformal metric are discussed, and the Chern-Simons and \(\eta\)- invariants for conformal structures on a closed hyperbolic 3-manifold. Reviewer: A.Aeppli (Minneapolis) Cited in 3 ReviewsCited in 5 Documents MSC: 53A30 Conformal differential geometry (MSC2010) 58D29 Moduli problems for topological structures Keywords:conformal manifold; biholomorphically invariant intrinsic pseudo-metric; Kobayashi conformal metric PDFBibTeX XMLCite \textit{B. N. Apanasov}, Int. J. Math. 2, No. 4, 361--382 (1991; Zbl 0761.53010) Full Text: DOI