Abstract.
In correspondence with the manifolds of quasi-constant sectional curvature defined (cf [5], [9]) in the Riemannian context, we introduce in the Kählerian 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, Kähler η-Einstein or Kähler-Einstein, etc. The characteristic classes are studied at the end and some examples are provided throughout.
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Bejan, CL., Benyounes, M. Kähler manifolds of quasi-constant holomorphic sectional curvature. J. geom. 88, 1–14 (2008). https://doi.org/10.1007/s00022-007-1934-7
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DOI: https://doi.org/10.1007/s00022-007-1934-7