An extension of the (1,2)-symplectic property for $ f$-structures on flag manifolds

Cohen, Nir; Pinzón, Sofía

doi:10.1070/im2008v072n03abeh002408

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Cited by 2 publications

(2 citation statements)

References 21 publications

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“…In this section we set up our notation and present the standard theory of partial (or generalized) flag manifolds associated with semisimple Lie algebras, see for example [15], [8], for similar description of flag manifolds.…”

Section: Preliminariesmentioning

confidence: 99%

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

Alves

Silva

2018

B Soc Paran Mat

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It is well known that the Einstein equation on a Riemannian flag manifold (G/K, g) reduces to an algebraic system if g is a G-invariant metric. In this paper we obtain explicitly new invariant Einstein metrics on generalized flag manifolds of Sp(n) and SO(2n); and we compute the Einstein system for generalized flag manifolds of type Sp(n). We also consider the isometric problem for these Einstein metrics.

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Section: Preliminariesmentioning

confidence: 99%

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

Alves

Silva

2018

B Soc Paran Mat

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“…In this section we set up our notation and present the standard theory of partial flag manifolds associated with semisimple Lie algebras (see, for example, [11], [6]).…”

Section: Preliminariesmentioning

confidence: 99%

Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds

Alves¹,

Silva²

2014

Preprint

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It is well known that the Einstein equation on a Riemannian flag manifold (G/K, g) reduces to a algebraic system, if g is a G-invariant metric. In this paper we described this system for all flag manifolds of a classical Lie group. We also determined the number of isotropy summands for all of these spaces and proved certain properties of the set of t-roots for flag manifolds of type Bn, Cn and Dn.

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An extension of the (1,2)-symplectic property for $ f$-structures on flag manifolds

Abstract: The (1, 1)-symplectic property for f -structures on a complex Riemannian manifold M is a natural extension of the (1, 2)-symplectic property for almost-complex structures on M , and arises in the analysis of complex harmonic maps with values in M .

Cited by 2 publications

References 21 publications

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds

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