scholarly journals Complete Kähler manifolds with zero Ricci curvature and Kobayashi-Ochiai's characterizationof complex projective spaces

1993 ◽  
Vol 69 (1) ◽  
pp. 1-4
Author(s):  
Ryoichi Kobayashi
Keyword(s):  
Ricci Curvature ◽  
Projective Spaces ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Complex Projective Spaces ◽  
Complex Projective

scholarly journals On the Optimal Volume Upper Bound for Kähler Manifolds with Positive Ricci Curvature (with an Appendix by Yuchen Liu)

2020 ◽  
Author(s):  
Kewei Zhang
Keyword(s):  
Projective Space ◽  
Ricci Curvature ◽  
Upper Bound ◽  
Complex Projective Space ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Positive Ricci Curvature ◽  
Complex Projective

Abstract Using $\delta $-invariants and Newton–Okounkov bodies, we derive the optimal volume upper bound for Kähler manifolds with positive Ricci curvature, from which we get a new characterization of the complex projective space.

scholarly journals Strongly not relatives Kähler manifolds

2017 ◽  
Vol 4 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Michela Zedda
Keyword(s):  
Projective Space ◽  
Positive Constant ◽  
Complex Projective Space ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Infinite Dimensional ◽  
Kahler Manifold ◽  
Hartogs Domains ◽  
Complex Projective

Abstract In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.

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