On harmonic maps between generalized flag manifolds

1992 ◽  
Vol 8 (1) ◽  
pp. 1-16
Author(s):  
Hou Zixin
Keyword(s):  
Harmonic Maps ◽  
Flag Manifolds ◽  
Generalized Flag Manifolds

Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics

2011 ◽  
Vol 10 (2) ◽  
pp. 307-325 ◽  
Author(s):  
Caio J. C. Negreiros ◽  
Lino Grama ◽  
Neiton P. da Silva
Keyword(s):  
Einstein Metrics ◽  
Harmonic Maps ◽  
Flag Manifolds

Equi-harmonic maps and Plücker formulae for horizontal-holomorphic curves on flag manifolds

2013 ◽  
Vol 193 (4) ◽  
pp. 1089-1102
Author(s):  
Lino Grama ◽  
Caio J. C. Negreiros ◽  
Luiz A. B. San Martin
Keyword(s):  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Flag Manifolds

Generalized flag manifolds as framed boundaries

1975 ◽  
Vol 142 (2) ◽  
pp. 191-193 ◽  
Author(s):  
Harsh V. Pittie ◽  
Larry Smith
Keyword(s):  
Flag Manifolds ◽  
Generalized Flag Manifolds

scholarly journals HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH FIVE ISOTROPY SUMMANDS

2013 ◽  
Vol 24 (10) ◽  
pp. 1350077 ◽  
Author(s):  
ANDREAS ARVANITOYEORGOS ◽  
IOANNIS CHRYSIKOS ◽  
YUSUKE SAKANE
Keyword(s):  
Einstein Equation ◽  
Einstein Metrics ◽  
Flag Manifold ◽  
Polynomial Systems ◽  
Flag Manifolds ◽  
Isotropy Representation ◽  
Generalized Flag Manifolds ◽  
A New Technique ◽  
Kähler Einstein Metrics ◽  
Homogeneous Einstein Metrics

We construct the homogeneous Einstein equation for generalized flag manifolds G/K of a compact simple Lie group G whose isotropy representation decomposes into five inequivalent irreducible Ad (K)-submodules. To this end, we apply a new technique which is based on a fibration of a flag manifold over another such space and the theory of Riemannian submersions. We classify all generalized flag manifolds with five isotropy summands, and we use Gröbner bases to study the corresponding polynomial systems for the Einstein equation. For the generalized flag manifolds E6/(SU(4) × SU(2) × U(1) × U(1)) and E7/(U(1) × U(6)) we find explicitly all invariant Einstein metrics up to isometry. For the generalized flag manifolds SO (2ℓ + 1)/( U (1) × U (p) × SO (2(ℓ - p - 1) + 1)) and SO (2ℓ)/( U (1) × U (p) × SO (2(ℓ - p - 1))) we prove existence of at least two non-Kähler–Einstein metrics. For small values of ℓ and p we give the precise number of invariant Einstein metrics.

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