Finding:

1. close

   Manifold

   Schemes are likewise glued together from affine schemes, which are a generalization of algebraic varieties. Both are related to manifolds, but are constructed algebraically using sheaves instead of atlases.
2. close

   Michael Atiyah

   Atiyah proved a generalization of this that applies to all compact symplectic manifolds acted on by a torus, showing that the image of the manifold under the moment map is a convex polyhedron, and with Pressley gave a related generalization to infinite dimensional loop groups.
3. close

   Differentiable manifold

   Many of the techniques from multivariate calculus also apply, mutatis mutandis, to differentiable manifolds. ... The exterior calculus allows for a generalization of the gradient, divergence and curl operators.
4. close

   Classification of manifolds

   From the point of view of category theory, the classification of manifolds is one piece of understanding the category: it's classifying the objects.
5. close

   History of manifolds and varieties

   In the modern theory of manifolds, these notions correspond to manifolds with constant, negative and positive curvature, respectively.
6. close

   Calabi–Yau manifold

   In the generalization to non-compact manifolds, the difference must vanish asymptotically. ... All hyper-Kähler manifolds are Calabi-Yau.
7. close

   Orbifold

   In the mathematical disciplines of topology and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold. ... Calabi-Yau manifolds
8. close

   Holonomy

   Sharpe, R.W. (1997), Differential Geometry: Cartan's Generalization of Klein's Erlangen Program, Springer-Verlag, New York, ISBN 0-387-94732-9 ... Structures on manifolds
9. close

   Haken manifold

   Applications The hierarchy makes proving certain kinds of theorems about Haken manifolds a matter of induction.
10. close

    Pseudo-Riemannian manifold

    In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold. ... Manifolds

Explore the following pages on Powerset:

• Manifold,
• Michael Atiyah,
• Differentiable manifold,
• Classification of manifolds,
• History of manifolds and varieties,
• Calabi–Yau manifold,
• Orbifold,
• Holonomy,
• Haken manifold,
• Pseudo-Riemannian manifold