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

scholarly journals Quasi-potentials and Kähler–Einstein Metrics on Flag Manifolds

1997 ◽  
Vol 196 (2) ◽  
pp. 620-629 ◽  
Author(s):  
H. Azad ◽  
R. Kobayashi ◽  
M.N. Qureshi
Keyword(s):  
Einstein Metrics ◽  
Flag Manifolds ◽  
Kähler Einstein Metrics

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.

scholarly journals The Ricci flow approach to homogeneous Einstein metrics on flag manifolds

2011 ◽  
Vol 61 (8) ◽  
pp. 1587-1600 ◽  
Author(s):  
Stavros Anastassiou ◽  
Ioannis Chrysikos
Keyword(s):  
Ricci Flow ◽  
Einstein Metrics ◽  
Flag Manifolds ◽  
Homogeneous Einstein Metrics

scholarly journals Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation

2013 ◽  
Vol 55 ◽  
pp. 59-71 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Ioannis Chrysikos ◽  
Yusuke Sakane
Keyword(s):  
Symbolic Computation ◽  
Einstein Metrics ◽  
Flag Manifolds ◽  
Homogeneous Einstein Metrics
Sign in / Sign up

Export Citation Format

Share Document