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The Stiefel manifold can be equipped with a uniform measure, i.e. a Borel measure that is invariant under the action of the groups noted above. For example, V 1 ( R 2 ) {\displaystyle V_{1}(\mathbb {R} ^{2})} which is isomorphic to the unit circle in the Euclidean plane, has as its uniform measure the natural uniform measure ( arc length ) on ...
The set of k-frames (particularly the set of orthonormal k-frames) in a given vector space X is known as the Stiefel manifold, and denoted V k (X). A k-frame defines a parallelotope (a generalized parallelepiped); the volume can be computed via the Gram determinant.
Stiefel-Whitney surfaces and decompositions of 3-manifolds into handlebodies, Topology Appl. 60 (1994), 267-280. J.C. Gómez Larrañaga, W. Heil, V.M. Núñez. Stiefel-Whitney surfaces and the trigenus of non-orientable 3-manifolds, Manuscripta Math. 100 (1999), 405-422.
The Stiefel–Whitney numbers of the tangent bundle of a smooth manifold are called the Stiefel–Whitney numbers of the manifold. They are known to be cobordism invariants. It was proven by Lev Pontryagin that if B is a smooth compact ( n +1)–dimensional manifold with boundary equal to M , then the Stiefel-Whitney numbers of M are all zero ...
Pages in category "Manifolds" The following 94 pages are in this category, out of 94 total. ... Stiefel manifold; Submanifold; T. Tame manifold; Tameness theorem;
In the special case in which E is the tangent bundle TM over the base manifold M, if a spin structure exists then one says that M is a spin manifold. Equivalently M is spin if the SO( n ) principal bundle of orthonormal bases of the tangent fibers of M is a Z 2 quotient of a principal spin bundle.
The flow in manifolds is extensively encountered in many industrial processes when it is necessary to distribute a large fluid stream into several parallel streams, or to collect them into one discharge stream, such as in fuel cells, heat exchangers, radial flow reactors, hydronics, fire protection, and irrigation. Manifolds can usually be ...
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