Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 6th 2015

    Created Sasakian manifold. This seems vaguely related to conifold/G 2G_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.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2015


    I have added some more hyperlinks, and formatting.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 6th 2015

    I added a reference that discusses 3-Sasakian 7-manifolds and how they carry interesting G 2G_2-structures.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 6th 2015

    Note that the example given in Wikipedia of a conifold is exactly the Riemannian cone over the Sasakian manifold S 3×S 2S^3\times S^2.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 30th 2019
    • (edited Mar 30th 2019)

    added pointer to

    for general purpose, and to

    • Beniamino Cappelletti-Montano, Giulia Dileo, Nearly Sasakian geometry and SU(2)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

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2019
    • (edited Apr 4th 2019)

    [ 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:

    • Charles Boyer, Krzysztof Galicki, Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, 2007
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2019

    The introduction to

    • Charles Boyer, Krzysztof Galicki, Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, 2007

    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.