On the quaternionic manifolds whose twistor spaces are Fano manifolds

Radu Pantilie

On the quaternionic manifolds whose twistor spaces are Fano manifolds

Differential Geometry 2014-11-20 v2 Algebraic Geometry

Authors: Radu Pantilie

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 $Sp(1) \times GL(k,H)$ 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.

Keywords

quaternionic manifold twistor space Fano manifold holonomy reduction quaternionic-Kaehler manifold Betti numbers

Cite

@article{arxiv.1411.2225,
  title  = {On the quaternionic manifolds whose twistor spaces are Fano manifolds},
  author = {Radu Pantilie},
  journal= {arXiv preprint arXiv:1411.2225},
  year   = {2014}
}

Comments

Tohoku Mathematical Journal (to appear), 5 pages

On the quaternionic manifolds whose twistor spaces are Fano manifolds

Abstract

Keywords

Cite

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