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Что (кто) такое Grassman manifold - определение

A SPACE OF LINEAR SUBSPACES OF A FIXED VECTOR SPACE

Grassman manifold; Grassmann manifold; Grassmanian; Grassmannians; Grassmannian manifold; Grassmannian variety

Grassmannian

In mathematics, the Grassmannian is a space that parameterizes all -dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective space of one dimension lower than .

https://en.wikipedia.org/wiki/Grassmannian

G2 manifold

SEVEN-DIMENSIONAL RIEMANNIAN MANIFOLD WITH HOLONOMY GROUP CONTAINED IN G2

Joyce manifold; G2-manifold

In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G_2 is one of the five exceptional simple Lie groups.

https://en.wikipedia.org/wiki/G2_manifold

Differentiable manifold

MANIFOLD UPON WHICH IT IS POSSIBLE TO PERFORM CALCULUS (ANY DIFFERENTIABLITY CLASS)

Differential manifold; Smooth manifold; Smooth manifolds; Differentiable manifolds; Manifold/rewrite/differentiable manifold; Differental manifold; Sheaf of smooth functions; Geometric structure; Ambient manifold; Non-smoothable manifold; Curved manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas).

https://en.wikipedia.org/wiki/Differentiable_manifold

Википедия

Grassmannian

In mathematics, the Grassmannian Gr(k, V) is a space that parameterizes all k-dimensional linear subspaces of the n-dimensional vector space V. For example, the Grassmannian Gr(1, V) is the space of lines through the origin in V, so it is the same as the projective space of one dimension lower than V.

When V is a real or complex vector space, Grassmannians are compact smooth manifolds. In general they have the structure of a smooth algebraic variety, of dimension $k(n-k).$

The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of projective lines in projective 3-space, equivalent to Gr(2, R⁴) and parameterized them by what are now called Plücker coordinates. Hermann Grassmann later introduced the concept in general.

Notations for the Grassmannian vary between authors; notations include Gr_k(V), Gr(k, V), Gr_k(n), or Gr(k, n) to denote the Grassmannian of k-dimensional subspaces of an n-dimensional vector space V.

https://en.wikipedia.org/wiki/Grassmannian