On the Geometry of Complex Hypersurfaces with Vanishing Bochner Curvature in Kählerian Spaces

Abstract

The study of complex hypersurfaces in Kählerian manifolds is a subject of profound interest in differential geometry and complex analysis. Among the various curvature tensors, the Bochner curvature tensor offers a nuanced perspective on the geometric structure of such spaces. This paper investigates complex hypersurfaces within Kählerian spaces that possess a vanishing Bochner curvature tensor. Special attention is given to the conditions under which these hypersurfaces exhibit totally geodesic behavior. The results contribute new insights into the interplay between curvature conditions and the intrinsic geometry of Kählerian manifolds.