Abstract
In correspondence with the manifolds of quasi-constant sectional curvature defined (cf [5], [9]) in the Riemannian context, we introduce in the Kahlerian framework the geometric notion of quasi-constant holomorphic sectional curvature. Some characterizations and properties are given. We obtain necessary and sufficient conditions for these manifolds to be locally symmetric, Ricci or Bochner flat, Kahler η-Einstein or Kahler-Einstein, etc. The characteristic classes are studied at the end and some examples are provided throughout.
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