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On the quaternionic manifolds whose twistor spaces are Fano manifolds | Radu Pantilie
; | Date: |
9 Nov 2014 | Abstract: | Let $M$ be a quaternionic manifold, $dim M=4k$, whose twistor space is a
Fano manifold. We prove the following: (a) $M$ admits a reduction to $Sp(1)
imes GL(k,H)$ if and only if $M=HP^k$, (b) either $b_2(M)=0$ or
$M=Gr_2(k+2,C)$. This generalizes results of S. Salamon and C.R. LeBrun,
respectively, who obtained the same conclusions under the assumption that $M$
is a complete quaternionic-Kaehler manifold with positive scalar curvature. | Source: | arXiv, 1411.2225 | Services: | Forum | Review | PDF | Favorites |
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