Some Geometric Problems of Conformally Compact Einstein Manifolds

2013 ◽  
pp. 184-195
Author(s):  
Yuguang Shi
Keyword(s):  
Einstein Manifolds ◽  
Geometric Problems ◽  
Conformally Compact

scholarly journals On the renormalized volumes for conformally compact Einstein manifolds

2008 ◽  
Vol 149 (6) ◽  
pp. 1755-1769 ◽  
Author(s):  
P. Yang ◽  
S. -Yu. A. Chang ◽  
J. Qing
Keyword(s):  
Einstein Manifolds ◽  
Conformally Compact

scholarly journals Quaternionic contact 4n + 3-manifolds and their 4n-quotients

2021 ◽  
Author(s):  
Yoshinobu Kamishima
Keyword(s):  
Scalar Curvature ◽  
Lie Group ◽  
Contact Structure ◽  
Einstein Manifolds ◽  
Hermitian Metrics ◽  
Kähler Metric ◽  
Formula One ◽  
Quaternion Space ◽  
Kahler Metric ◽  
Do So

AbstractWe study some types of qc-Einstein manifolds with zero qc-scalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics $$(g_a,\{J_\alpha \}_{\alpha =1}^3)$$ ( g a , { J α } α = 1 3 ) on the domain Y of the standard quaternion space $${\mathbb {H}}^n$$ H n one of which, say $$(g_a,J_1)$$ ( g a , J 1 ) is a Bochner flat Kähler metric. To do so, we deform conformally the standard quaternionic contact structure on the domain X of the quaternionic Heisenberg Lie group$${{\mathcal {M}}}$$ M to obtain quaternionic Hermitian metrics on the quotient Y of X by $${\mathbb {R}}^3$$ R 3 .

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