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Created Sasakian manifold. This seems vaguely related to conifold/$G_2$-manifold stuff, but the state of the art in the Sasakian world seems very much experimental: difficult to find any large families of such structures.
Thanks!
I have added some more hyperlinks, and formatting.
I added a reference that discusses 3-Sasakian 7-manifolds and how they carry interesting $G_2$-structures.
Note that the example given in Wikipedia of a conifold is exactly the Riemannian cone over the Sasakian manifold $S^3\times S^2$.
added pointer to
for general purpose, and to
Beniamino Cappelletti-Montano, Giulia Dileo, Nearly Sasakian geometry and $SU(2)$-structures (arXiv:1410.0942)
Anna Fino, Hypo contact and Sasakian structures on Lie groups, talk at Workshop on CR and Sasakian Geometry, Luxembourg– 24 - 26 March 2008 (pdf)
for relation to SU(2)-structure
also to
[ sending this by hand – the automatic announcement mechanisn is down! ]
added pointer to the original references
Shigeo Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure I, Tohoku Math. J. (2) 12 (1960), 459-476 (euclid:1178244407)
Shigeo Sasaki, Y. Hatakeyama, On differentiable manifolds with contact metric structures, J. Math. Soc. Japan 14 (1962), 249-271 (euclid:1261060580)
Shigeo Sasaki, Almost contact manifolds, Part 1, Lecture Notes, Mathematical Institute, Tohoku University (1965).
Shigeo Sasaki, Almost contact manifolds, Part 2, Lecture Notes, Mathematical Institute, Tohoku University (1967).
Shigeo Sasaki, Almost contact manifolds, Part 3, Lecture Notes, Mathematical Institute, Tohoku University (1968).
and to this modern textbook:
The introduction to
is a good read: mathematical insight, personal tragedy, arguments for a major blind spot of the community, all nicely laid out on the first few pages.
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