Einstein metrics and quaternionic Kähler manifolds

1992 ◽  
Vol 210 (1) ◽  
pp. 305-325 ◽  
Author(s):  
McKenzie Y. Wang
Keyword(s):  
Einstein Metrics ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Quaternionic Kähler

scholarly journals Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

2021 ◽  
Author(s):  
V. Cortés ◽  
A. Saha ◽  
D. Thung
Keyword(s):  
Curvature Tensor ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Cohomogeneity One ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

Quaternionic maps between quaternionic Kähler manifolds

2005 ◽  
Vol 250 (3) ◽  
pp. 523-537
Author(s):  
Jiayu Li ◽  
Xi Zhang
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Quaternionic Kähler

Singular Quaternionic Kähler Manifolds

1996 ◽  
pp. 163-170
Author(s):  
Demir N. Kupeli
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Quaternionic Kähler

scholarly journals Geometric estimates for complex Monge–Ampère equations

2020 ◽  
Vol 2020 (765) ◽  
pp. 69-99 ◽  
Author(s):  
Xin Fu ◽  
Bin Guo ◽  
Jian Song
Keyword(s):  
Einstein Metrics ◽  
Kähler Manifolds ◽  
Singular Solutions ◽  
Kahler Manifolds ◽  
Diameter Estimate ◽  
Uniform Diameter ◽  
Kähler Einstein Metrics ◽  
Geometric Regularity ◽  
Monge Ampere ◽  
Geometric Estimates

AbstractWe prove uniform gradient and diameter estimates for a family of geometric complex Monge–Ampère equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge–Ampère equations. We also prove a uniform diameter estimate for collapsing families of twisted Kähler–Einstein metrics on Kähler manifolds of nonnegative Kodaira dimensions.

scholarly journals Hyperkähler cones and instantons on quaternionic Kähler manifolds

2020 ◽  
Vol 58 (3) ◽  
pp. 291-323
Author(s):  
Chandrashekar Devchand ◽  
Massimiliano Pontecorvo ◽  
Andrea Spiro
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Quaternionic Kähler

scholarly journals Vector bundles over quaternionic Kähler manifolds

1988 ◽  
Vol 40 (3) ◽  
pp. 425-440 ◽  
Author(s):  
Takashi Nitta
Keyword(s):  
Vector Bundles ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Quaternionic Kähler
Sign in / Sign up

Export Citation Format

Share Document