On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces. (English) Zbl 1109.53019

Slovák, Jan (ed.) et al., The proceedings of the 24th winter school “Geometry and physics”, Srní, Czech Republic, January 17–24, 2004. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 75, 309-316 (2005).
An equiaffine space is a manifold \(A_n\) with an affine connection whose Ricci tensor is symmetric. The authors study equiaffine spaces admitting an holomorphically projective map \(f: A_n\to K_n\), \(K_n\) denoting a Kähler space. Assume that the Ricci tensor of \(A_n\) preserves the almost complex structure induced on \(A_n\), via \(f\), by the Kähler structure on \(K_n\). If \(A_n\) is semisymmetric, then \(K_n\) is quasisymmetric or has constant holomorphic sectional curvature. Furthermore, if \(A_n\) is a recurrent space, then \(A_n\) is flat and \(K_n\) has constant holomorphic sectional curvature.
For the entire collection see [Zbl 1074.53001].


53B20 Local Riemannian geometry
53B05 Linear and affine connections
53B35 Local differential geometry of Hermitian and Kählerian structures