Skip to main content
MathOverflow

Return to Question

minor cleanup
Source Link
user9072
user9072

Homogeneous Quaternionic-K\"aherKähler Structure of the Grassmannians?

Paraphrasing from Cortes' notes:

The quaternionic K"ahlerKähler condition for a manifold $M$, means that End$(T(M))$$\operatorname{End}(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symm.symmetric almost complex structures.

Now the Grassmannians $Gr[p+2,2]$$\operatorname{Gr}[p+2,2]$ are examples of quaternionic K"ahlerKähler manifolds, and of homogeneous spaces. Is $Q(Gr[p+2,2])$$Q(\operatorname{Gr}[p+2,2])$ an $U(p+2)$-equivariant vector bundle?

Homogeneous Quaternionic-K\"aher Structure of the Grassmannians?

Paraphrasing from Cortes' notes:

The quaternionic K"ahler condition for a manifold $M$, means that End$(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symm. almost complex structures.

Now the Grassmannians $Gr[p+2,2]$ are examples of quaternionic K"ahler manifolds, and of homogeneous spaces. Is $Q(Gr[p+2,2])$ an $U(p+2)$-equivariant vector bundle?

Homogeneous Quaternionic-Kähler Structure of the Grassmannians?

Paraphrasing from Cortes' notes:

The quaternionic Kähler condition for a manifold $M$, means that $\operatorname{End}(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symmetric almost complex structures.

Now the Grassmannians $\operatorname{Gr}[p+2,2]$ are examples of quaternionic Kähler manifolds, and of homogeneous spaces. Is $Q(\operatorname{Gr}[p+2,2])$ an $U(p+2)$-equivariant vector bundle?

added 5 characters in body
Source Link
Pavel Katzo
Pavel Katzo
  • 181
  • 4

Paraphrasing from Cortes' notes:

The quaternionic K"ahler condition for a manifold $M$, means that End$(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symm. almost complex structures.

Now the Grassmannians $Gr[p+2,2]$ are examples of quaternionic K"ahler manifolds, and of homogeneous spaces. Is $Q(Gr[p+2,2])$ and equivariantan $U(p+2)$-equivariant vector bundle?

Paraphrasing from Cortes' notes:

The quaternionic K"ahler condition for a manifold $M$, means that End$(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symm. almost complex structures.

Now the Grassmannians $Gr[p+2,2]$ are examples of quaternionic K"ahler manifolds, and of homogeneous spaces. Is $Q(Gr[p+2,2])$ and equivariant vector bundle?

Paraphrasing from Cortes' notes:

The quaternionic K"ahler condition for a manifold $M$, means that End$(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symm. almost complex structures.

Now the Grassmannians $Gr[p+2,2]$ are examples of quaternionic K"ahler manifolds, and of homogeneous spaces. Is $Q(Gr[p+2,2])$ an $U(p+2)$-equivariant vector bundle?

Source Link
Pavel Katzo
Pavel Katzo
  • 181
  • 4

Homogeneous Quaternionic-K\"aher Structure of the Grassmannians?

Paraphrasing from Cortes' notes:

The quaternionic K"ahler condition for a manifold $M$, means that End$(T(M))$ admits a parallel subbundle $Q$ which is locally spanned by $3$ anticommuting skew-symm. almost complex structures.

Now the Grassmannians $Gr[p+2,2]$ are examples of quaternionic K"ahler manifolds, and of homogeneous spaces. Is $Q(Gr[p+2,2])$ and equivariant vector bundle?