The Holomorphic Sectional Curvature of General Natural KÄhler Structures on Cotangent Bundles

2008/10/09 by S. L. Druta, Druta, S. L.
Mathematics · Physics and Astronomy · #53C07 #53C15 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C07 #msc:53C15 #msc:53C55

paper · pdf · doi:10.48550/arxiv.0810.1652

14 pages

arxiv created 2008/10/09 · openalex publication_date 2008/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the conditions under which a Kählerian structure (G,J) of general natural lift type on the cotangent bundle T^*M of a Riemannian manifold (M,g) has constant holomorphic sectional curvature. We obtain that a certain parameter involved in the condition for (T^*M,G,J) to be a Kählerian manifold, is expressed as a rational function of the other two, their derivatives, the constant sectional curvature of the base manifold (M,g), and the constant holomorphic sectional curvature of the general natural Kählerian structure (G,J).

Citations

• A locally symmetric Kaehler Einstein structure on a tube in the nonzero cotangent bundle of a space form

Related

• Kahler-Einstein Structures of General Natural Lifted Type on the Cotangent Bundles
• Cotangent Bundles with General Natural Kahler Structures
• A class of Kaehler Einstein structures on the cotangent bundle
• A Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold
• A canonical structure on the tangent bundle of a pseudo- or para-Kähler manifold