Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds

1991 ◽  
Vol 290 (1) ◽  
pp. 689-712 ◽  
Author(s):  
László Lempert ◽  
Róbert Szőke
Keyword(s):  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Global Solutions ◽  
Complex Structures ◽  
Homogeneous Complex ◽  
Monge Ampere

scholarly journals Monge–Ampère Equations on Riemannian Manifolds

1996 ◽  
Vol 132 (1) ◽  
pp. 126-139 ◽  
Author(s):  
Bo Guan ◽  
YanYan Li
Keyword(s):  
Riemannian Manifolds ◽  
Monge Ampere

scholarly journals A Kähler Einstein structure on the tangent bundle of a space form

2001 ◽  
Vol 25 (3) ◽  
pp. 183-195 ◽  
Author(s):  
Vasile Oproiu
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Negative Curvature ◽  
Space Form ◽  
Positive Curvature ◽  
Holomorphic Sectional Curvature ◽  
Zero Section ◽  
Constant Negative Curvature ◽  
Constant Positive Curvature

We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive curvature.

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