Geodesic
B-connections and Their Conformal Invariants on Conformally Kaehler Manifolds with B-metric
Publications de l'Institut Mathématique, _N_S_42 (1987) no. 56, p. 107

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On a Kaehler manifold there is not a complete analogue of the conformal geometry on a Riemannian manifold. In this paper, we consider a class of complex manifolds with B-metric (including Kaehler manifolds with B-metric). The general conformal group and its special subgroups are determined. The Bochner curvature tensor of the manifold is shown to be a conformal invariant. The zero Bochner curvature tensor is proved to be an integrability condition of a geometrical system of partial differential equations and a characterization condition of a conformally flat manifold. Holomorphically umbilic submanifolds (Holomorphic spheres) are conformal invariants. The manifolds satisfying the axiom of holomorphic spheres are also characterized by zero Bochner curvature tensor. Thus, on the considered manifolds, there is a complete analogue of the conformal geometry on a Riemannian manifold.
Classification : 55B05 
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     author = {Georgi Ganchev and Kostadin Gribachev and Vesselka Mihova},
     title = {B-connections and {Their} {Conformal} {Invariants} on {Conformally} {Kaehler} {Manifolds} with {B-metric}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {107 },
     publisher = {mathdoc},
     volume = {_N_S_42},
     number = {56},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1987_N_S_42_56_a12/}
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Georgi Ganchev; Kostadin Gribachev; Vesselka Mihova. B-connections and Their Conformal Invariants on Conformally Kaehler Manifolds with B-metric. Publications de l'Institut Mathématique, _N_S_42 (1987) no. 56, p. 107 . http://geodesic.mathdoc.fr/item/PIM_1987_N_S_42_56_a12/