Abstract
A classification of locally quaternion Kähler manifolds M 4n with positive scalar curvature is obtained as a consequence of J. Wolf's work on space forms of irreducible symmetric spaces. We determine the Betti numbers of such manifolds M 4n as well as of the “projective” 3-Sasakian manifolds fibering over them. We study the geometry of the quaternion Kähler and locally quaternion Kähler submanifolds for each M 4n, which is particularly significant for 4n = 16 due to its relation with four quaternionic structures on the Grassmannian \(\overline {{\text{Gr}}} _4 \) (R 8).
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Piccinni, P. The Geometry of Positive Locally Quaternion Kähler Manifolds. Annals of Global Analysis and Geometry 16, 255–272 (1998). https://doi.org/10.1023/A:1006520217385
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DOI: https://doi.org/10.1023/A:1006520217385