scholarly journals The First Eigenvalue of the Dirac Operator on Quaternionic Kähler Manifolds

1998 ◽  
Vol 199 (2) ◽  
pp. 327-349 ◽  
Author(s):  
W. Kramer ◽  
U. Semmelmann ◽  
G. Weingart
Keyword(s):  
Dirac Operator ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Quaternionic Kähler

scholarly journals A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds

2013 ◽  
Vol 6 (5) ◽  
pp. 1001-1012
Author(s):  
Vincent Guedj ◽  
Boris Kolev ◽  
Nader Yeganefar
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
First Eigenvalue ◽  
Convex Domains ◽  
The First Eigenvalue

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.

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