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It's all in the title: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this post by Moroianu, where he says that

the quaternionic projective spaces $ℍP_n$ are quaternion-Kähler, but have no almost complex structure

I now think my assumption is probably false. Can someone please help "de-confuse" me?

It's all in the title: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this post by Moroianu, where he says that

the quaternionic projective spaces $ℍP_n$ are quaternion-Kähler, but have no almost complex structure

I now think my assumption is probably false. Can someone please help "de-confuse" me?

It's all in the title: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this  post by Moroaniu, where he says that

the quaternionic projective spaces ℍPn are quaternion-K"ahler, but have no almost complex structure

I now think my assumption is probably false. Can someone please help "de-confuse" me?

It's all in the title: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this post by Moroianu, where he says that

the quaternionic projective spaces $ℍP_n$ are quaternion-Kähler, but have no almost complex structure

I now think my assumption is probably false. Can someone please help "de-confuse" me?

It's all in the title I guess: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this post by Moroaniu, where he says that

the quaternionic projective spaces ℍPn are quaternion-K"ahler, but have no almost complex structure

I now think my assumption is probably false. Can someone please help "de-confuse" me?

It's all in the title: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this post by Moroaniu, where he says that

the quaternionic projective spaces ℍPn are quaternion-K"ahler, but have no almost complex structure

I now think my assumption is probably false. Can someone please help "de-confuse" me?