General Mathematics, Vol. 5, No. 1 - 4, pp. 297-310, 1995

V. Oproiu -- Some Kahler Structures on the Tangent Bundle of a Space Form

Abstract: Some K\"ahler structures are obtained on the tangent bundle of a Riemannian manifold of constant sectional curvature. If the constant sectional curvature is negative then the found K\"ahler structure is defined on the whole tangent bundle and is K\"ahler Einstein. If the constant sectional curvature is positive then a K\"ahler Einstein structure is defined in a tube around zero section in the tangent bundle. Moreover, the holomorphic sectional curvature of the obtained K\"ahler Einstein structure is constant. Two special cases are also studied.

Classification (MSC91): 53C15, 53C07, 53C55

Keywords: Tangent bundle, Kahler manifold, Kahler Einstein manifold, locally symmetric space.

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