Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology 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 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

1. • CommentRowNumber1.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 6th 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexCreated [[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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 6th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I have added some more hyperlinks, and formatting.

   Thanks!

   I have added some more hyperlinks, and formatting.

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 6th 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI added a reference that discusses 3-Sasakian 7-manifolds and how they carry interesting $G_2$-structures.

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

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 6th 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexNote that the example given [in Wikipedia](https://en.wikipedia.org/wiki/Conifold) of a [[conifold]] is exactly the Riemannian cone over the Sasakian manifold $S^3\times S^2$.

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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 30th 2019
   • (edited Mar 30th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[James Sparks]], _Sasaki-Einstein Manifolds_, Surv. Diff. Geom. 16 (2011) 265-324 ([arXiv:1004.2461](https://arxiv.org/abs/1004.2461)) for general purpose, and to * Beniamino Cappelletti-Montano, Giulia Dileo, _Nearly Sasakian geometry and $SU(2)$-structures_ ([arXiv:1410.0942](https://arxiv.org/abs/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](http://math.uni.lu/CRSasaki/slides/fino.pdf)) for relation to [[SU(2)-structure]] also to * [[José Figueroa-O'Farrill]], Andrea Santi, _Sasakian manifolds and M-theory_, Class. Quantum Grav. 33 (2016), 095004 ([arXiv:1511.03460](https://arxiv.org/abs/1511.03460)) <a href="https://ncatlab.org/nlab/revision/diff/Sasakian+manifold/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/Sasakian+manifold/6">v6</a>, <a href="https://ncatlab.org/nlab/show/Sasakian+manifold">current</a>

   added pointer to

   • James Sparks, Sasaki-Einstein Manifolds, Surv. Diff. Geom. 16 (2011) 265-324 (arXiv:1004.2461)

   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

   • José Figueroa-O’Farrill, Andrea Santi, Sasakian manifolds and M-theory, Class. Quantum Grav. 33 (2016), 095004 (arXiv:1511.03460)

   diff, v6, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 4th 2019
   • (edited Apr 4th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItex[ 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](https://projecteuclid.org/euclid.tmj/1178244407)) * [[Shigeo Sasaki]], Y. Hatakeyama, _On differentiable manifolds with contact metric structures_, J. Math. Soc. Japan 14 (1962), 249-271 ([euclid:1261060580](https://projecteuclid.org/euclid.jmsj/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

   [ 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
7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 4th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe 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.

   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.