nondegenerate manifold
1Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …
2Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… …
3Hermitian manifold — In mathematics, a Hermitian manifold is the complex analog of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define …
4Complex manifold — In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk[1] in Cn, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense… …
5Poisson manifold — In mathematics, a Poisson manifold is a differentiable manifold M such that the algebra of smooth functions over M is equipped with a bilinear map called the Poisson bracket, turning it into a Poisson algebra. Since their introduction by André… …
6Almost complex manifold — In mathematics, an almost complex manifold is a smooth manifold equipped with smooth linear complex structure on each tangent space. The existence of this structure is a necessary, but not sufficient, condition for a manifold to be a complex… …
7G2 manifold — A G 2 manifold is a seven dimensional Riemannian manifold with holonomy group G 2. The group G 2 is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper… …
8Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …
9Degenerate form — For other uses, see Degeneracy. In mathematics, specifically linear algebra, a degenerate bilinear form ƒ(x,y) on a vector space V is one such that the map from V to V * (the dual space of V) given by is not an isomorphism. An equivalent… …
10Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …
