HOMOGENEOUS EINSTEIN METRICS ON COMPLEX STIEFEL MANIFOLDS AND SPECIAL UNITARY GROUPS

2017 ◽  
Author(s):  
Andreas ARVANITOYEORGOS ◽  
Yusuke SAKANE ◽  
Marina STATHA
Keyword(s):  
Einstein Metrics ◽  
Unitary Groups ◽  
Stiefel Manifolds ◽  
Homogeneous Einstein Metrics

scholarly journals New homogeneous Einstein metrics on Stiefel manifolds

2014 ◽  
Vol 35 ◽  
pp. 2-18 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Yusuke Sakane ◽  
Marina Statha
Keyword(s):  
Einstein Metrics ◽  
Stiefel Manifolds ◽  
Homogeneous Einstein Metrics

scholarly journals New homogeneous Einstein metrics on quaternionic Stiefel manifolds

2018 ◽  
Vol 18 (4) ◽  
pp. 509-524 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Yusuke Sakane ◽  
Marina Statha
Keyword(s):  
Homogeneous Space ◽  
Einstein Metrics ◽  
Flag Manifold ◽  
Total Space ◽  
Stiefel Manifold ◽  
Isotropy Representation ◽  
Stiefel Manifolds ◽  
Generalized Flag Manifold ◽  
Generalized Wallach Space ◽  
Homogeneous Einstein Metrics

Abstract We consider invariant Einstein metrics on the quaternionic Stiefel manifold Vpℍn of all orthonormal p-frames in ℍn. This manifold is diffeomorphic to the homogeneous space Sp(n)/Sp(n − p) and its isotropy representation contains equivalent summands. We obtain new Einstein metrics on Vpℍn ≅ Sp(n)/Sp(n − p), where n = k1 + k2 + k3 and p = n − k3. We view Vpℍn as a total space over the generalized Wallach space Sp(n)/(Sp(k1)×Sp(k2)×Sp(k3)) and over the generalized flag manifold Sp(n)/(U(p)×Sp(n − p)).

Invariant Einstein metrics on $\mathrm{SU}(n)$ and complex Stiefel manifolds

2020 ◽  
Vol 72 (2) ◽  
pp. 161-210 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Yusuke Sakane ◽  
Marina Statha
Keyword(s):  
Einstein Metrics ◽  
Stiefel Manifolds

Homogeneous Einstein Finsler Metrics on -dimensional Spheres

2018 ◽  
Vol 62 (3) ◽  
pp. 509-523
Author(s):  
Libing Huang ◽  
Xiaohuan Mo
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Einstein Metrics ◽  
Constant Sectional Curvature ◽  
Einstein Metric ◽  
Finsler Metrics ◽  
Dimensional Sphere ◽  
Order Ordinary Differential Equation ◽  
Canonical Metric ◽  
Homogeneous Einstein Metrics

AbstractIn this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.

scholarly journals Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

2009 ◽  
Vol 61 (6) ◽  
pp. 1201-1213 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
V. V. Dzhepko ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Manifold ◽  
Positive Integer ◽  
Lie Groups ◽  
Einstein Metrics ◽  
Homogeneous Spaces ◽  
Classical Groups ◽  
Stiefel Manifolds ◽  
Additional Symmetries

Abstract A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics, with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l). Furthermore, we show that for any positive integer p there exists a Stiefelmanifold SO(n)/SO(l) that admits at least p SO(n)-invariant Einstein metrics.

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