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Almost parallel structures. (English) Zbl 1008.53043
Fernández, Marisa (ed.) et al., Global differential geometry: the mathematical legacy of Alfred Gray. Proceedings of the international congress on differential geometry held in memory of Professor Alfred Gray, Bilbao, Spain, September 18-23, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 288, 162-181 (2001).
The present paper is based on the lecture entitled “A Mathematical Tribute” given by the author at the conferences in memory of Alfred Gray in Bilbao in September 2000. It is an interesting survey of contributions of Alfred Gray and others on almost Hermitian manifolds, \(G_2\)-manifolds, curvature identities, volume expansions, plotting geodesics, and the geometry of nilmanifolds. Finally, the author constructs a new example of a compact 8-manifold with a quaternionic 4-form that is closed but not parallel.
For the entire collection see [Zbl 0980.00033].

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53-03 History of differential geometry
53C22 Geodesics in global differential geometry
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C30 Differential geometry of homogeneous manifolds
01A70 Biographies, obituaries, personalia, bibliographies
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