scholarly journals Diameter, volume, and topology for positive Ricci curvature

1991 ◽  
Vol 33 (3) ◽  
pp. 743-747 ◽  
Author(s):  
J.-H. Eschenburg
Keyword(s):  
Ricci Curvature ◽  
Positive Ricci Curvature ◽  
And Topology

scholarly journals Manifolds of low cohomogeneity and positive Ricci curvature

2010 ◽  
Vol 28 (3) ◽  
pp. 282-289 ◽  
Author(s):  
S. Bechtluft-Sachs ◽  
D.J. Wraith
Keyword(s):  
Ricci Curvature ◽  
Positive Ricci Curvature

On the Asymptotic Behavior of Complete Kähler Metrics of Positive Ricci Curvature

2010 ◽  
Vol 62 (1) ◽  
pp. 3-18
Author(s):  
Boudjemâa Anchouche
Keyword(s):  
Asymptotic Behavior ◽  
Line Bundle ◽  
Ricci Curvature ◽  
Projective Variety ◽  
Volume Form ◽  
Positive Ricci Curvature ◽  
Standard Type ◽  
Number Of Components ◽  
Holomorphic Sections ◽  
Volume Forms

AbstractLet (X, g) be a complete noncompact Kähler manifold, of dimension n ≥ 2, with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that X can be compactified, i.e., X is biholomorphic to a quasi-projective variety. The aim of this paper is to prove that the L2 holomorphic sections of the line bundle K−qXand the volume form of the metric g have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the Kähler metric g and of the Fubini-Study metric induced on X. In the case of dimC X = 2, we establish a relation between the number of components of the divisor D and the dimension of the.

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