scholarly journals M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds

2020 ◽  
Vol 36 (3) ◽  
pp. 336-353
Author(s):  
Yun Miao
Keyword(s):  
Curvature Tensor ◽  
Conformally Flat ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

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.

scholarly journals The duality of conformally flat manifolds

2011 ◽  
Vol 42 (1) ◽  
pp. 131-152 ◽  
Author(s):  
Huili Liu ◽  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

scholarly journals Twistor spinors on conformally flat manifolds

1997 ◽  
Vol 41 (3) ◽  
pp. 495-503 ◽  
Author(s):  
Wolfgang Kühnel ◽  
Hans–Bert Rademacher
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds
Sign in / Sign up

Export Citation Format

Share Document