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searching for Subbundle 35 found (58 total)

alternate case: subbundle

Ehresmann connection (3,155 words) [view diff] exact match in snippet view article find links to article

pushforward of tangent vectors. The horizontal spaces together form a vector subbundle of T E {\displaystyle TE} . This has the immediate benefit of being definable

Tautological bundle (2,441 words) [view diff] exact match in snippet view article find links to article

map is given as follows: since X is compact, any vector bundle E is a subbundle of a trivial bundle: E ↪ X × R n + k {\displaystyle E\hookrightarrow X\times

Carnot group (603 words) [view diff] exact match in snippet view article find links to article

The subbundle of the tangent bundle associated to this eigenspace is called horizontal. On a Carnot group, any norm on the horizontal subbundle gives

Linear connection (197 words) [view diff] exact match in snippet view article find links to article

in the horizontal direction" (i.e., the horizontal bundle is a vector subbundle of the tangent bundle of the fiber bundle), even if they are not "linear

Grassmann bundle (520 words) [view diff] exact match in snippet view article find links to article

natural vector bundles on it; namely, there are universal or tautological subbundle S and universal quotient bundle Q that fit into 0 → S → p ∗ E → Q → 0

Non-autonomous system (mathematics) (414 words) [view diff] exact match in snippet view article

bundle Q → R {\displaystyle Q\to \mathbb {R} } is represented by a closed subbundle of a jet bundle J r Q {\displaystyle J^{r}Q} of Q → R {\displaystyle Q\to

Unit tangent bundle (881 words) [view diff] exact match in snippet view article find links to article

with a Finsler metric F : TM → R, then the unit sphere bundle is the subbundle of the tangent bundle whose fiber at x is the indicatrix of F: U T x (

Metric-affine gravitation theory (1,258 words) [view diff] exact match in snippet view article find links to article

connection is associated to a principal connection on a Lorentz reduced subbundle F g X {\displaystyle F^{g}X} of the frame bundle F X {\displaystyle FX}

Stable vector bundle (1,887 words) [view diff] exact match in snippet view article find links to article

proper non-zero subbundles V of W and is semistable if μ ( V ) ≤ μ ( W ) {\displaystyle \mu (V)\leq \mu (W)} for all proper non-zero subbundles V of W. Informally

Higgs bundle (548 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varphi } -invariant subbundles must first be defined. In Hitchin's original discussion, a rank-1 subbundle labelled L is φ {\displaystyle \varphi

Projective bundle (1,373 words) [view diff] exact match in snippet view article find links to article

map p: P(E) → X is to specify a line subbundle of f*E. For example, taking f to be p, one gets the line subbundle O(-1) of p*E, called the tautological

Bundle (mathematics) (755 words) [view diff] exact match in snippet view article

is the fibre or fiber of the bundle over b. A bundle (E*, p*, B*) is a subbundle of (E, p, B) if B* ⊂ B, E* ⊂ E and p* = p|E*. A cross section is a map

Tractor bundle (1,327 words) [view diff] exact match in snippet view article find links to article

} , of signature ( p + 1 , q + 1 ) {\displaystyle (p+1,q+1)} , a line subbundle X ⊂ T {\displaystyle {\mathcal {X}}\subset {\mathcal {T}}} , a linear

Tensor product bundle (284 words) [view diff] exact match in snippet view article find links to article

that E ⊕ E' is trivial. Choose F' in the same way. Then let E ⊗ F be the subbundle of (E ⊕ E') ⊗ (F ⊕ F') with the desired fibers. Finally, use the approximation

Courant bracket (1,367 words) [view diff] exact match in snippet view article find links to article

maximal isotropic subspace. A Dirac structure is a maximally isotropic subbundle of T ⊕ T ∗ {\displaystyle {\mathbf {T} }\oplus {\mathbf {T} }^{*}} whose

Riemannian submersion (533 words) [view diff] exact match in snippet view article find links to article

e r ( d f ) ⊥ {\displaystyle \mathrm {ker} (df)^{\perp }} denotes the subbundle of T M {\displaystyle TM} that is the orthogonal complement of k e r (

Connection (composite bundle) (1,394 words) [view diff] exact match in snippet view article

h = h ∗ Y {\displaystyle Y^{h}=h^{*}Y} over X {\displaystyle X} is a subbundle of a fiber bundle Y → X {\displaystyle Y\to X} . For instance, let P →

Gauge gravitation theory (1,155 words) [view diff] exact match in snippet view article find links to article

closed subgroup H {\displaystyle H} , i.e., there exists a principal subbundle of P {\displaystyle P} with the structure group H {\displaystyle H} .

Affine gauge theory (1,940 words) [view diff] exact match in snippet view article find links to article

{\displaystyle FX} to A F X {\displaystyle AFX} onto a reduced principal subbundle which corresponds to the canonical structure of a vector bundle T X {\displaystyle

Lie group action (1,333 words) [view diff] exact match in snippet view article find links to article

the image of the infinitesimal action is actually equal to the vertical subbundle T π P ⊂ T P {\displaystyle T^{\pi }P\subset TP} . An important (and common)

Real projective space (2,083 words) [view diff] exact match in snippet view article find links to article

tautological bundle. More precisely, this is called the tautological subbundle, and there is also a dual n-dimensional bundle called the tautological

Flag bundle (254 words) [view diff] exact match in snippet view article find links to article

can be constructed inductively. Here, E i {\displaystyle E_{i}} is a subbundle not subsheaf of E i + 1 . {\displaystyle E_{i+1}.} William Fulton. (1998)

Cartan's equivalence method (1,252 words) [view diff] exact match in snippet view article find links to article

of a "prolongation". The most economical way to do this is to use a G-subbundle PM of the principal bundle of linear coframes LM, although this approach

Coherent sheaf (6,934 words) [view diff] exact match in snippet view article find links to article

{\mathcal {O}}_{X}} is a subsheaf but typically not a subbundle (since any line bundle has only two subbundles). The quasi-coherent sheaves on any fixed scheme

Ambient construction (1,058 words) [view diff] exact match in snippet view article find links to article

conformal metric defined on M. Let π : N → M denote the tautological subbundle of T*M ⊗ T*M defined by all representatives of the conformal metric. In

Convenient vector space (4,011 words) [view diff] exact match in snippet view article find links to article

bundle T N {\displaystyle TN} to f ( M ) {\displaystyle f(M)} into the subbundle normal to f ( M ) {\displaystyle f(M)} and tangential to f ( M ) {\displaystyle

Courant algebroid (1,583 words) [view diff] exact match in snippet view article find links to article

T^{*}M} ), a Dirac structure is a maximally isotropic integrable vector subbundle L → M {\displaystyle L\to M} , i.e. ⟨ L , L ⟩ ≡ 0 {\displaystyle \langle

Complex projective space (3,929 words) [view diff] exact match in snippet view article find links to article

called the tautological line bundle. It is equivalently defined as the subbundle of the product C n + 1 × C P n → C P n {\displaystyle \mathbf {C} ^{n+1}\times

Stable principal bundle (1,338 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathfrak {q}}\subset {\mathfrak {g}}} and can take the associated subbundle. In this case more care must be taken because the adjoint representation

Lie algebroid (7,376 words) [view diff] exact match in snippet view article find links to article

[ ⋅ , ⋅ ] , ρ ) {\displaystyle (A,[\cdot ,\cdot ],\rho )} is a vector subbundle A ′ → M ′ {\displaystyle A'\to M'} of the restriction A ∣ M ′ → M ′ {\displaystyle

Stiefel–Whitney class (4,071 words) [view diff] exact match in snippet view article find links to article

\gamma ^{n}\to Gr_{n},} a rank n vector bundle that can be defined as the subbundle of the trivial bundle of fiber V whose fiber at a point W ∈ G r n ( V

Stiefel–Whitney class (4,071 words) [view diff] exact match in snippet view article find links to article

\gamma ^{n}\to Gr_{n},} a rank n vector bundle that can be defined as the subbundle of the trivial bundle of fiber V whose fiber at a point W ∈ G r n ( V

Holonomy (5,911 words) [view diff] exact match in snippet view article find links to article

Thus H(p) is a reduced bundle for the connection. Furthermore, since no subbundle of H(p) is preserved by parallel transport, it is the minimal such reduction

Quadric (algebraic geometry) (3,537 words) [view diff] exact match in snippet view article

O(0,−1). The spinor bundle on a quadric 3-fold X is the natural rank-2 subbundle on X viewed as the isotropic Grassmannian of 2-planes in a 4-dimensional

Riemannian connection on a surface (10,206 words) [view diff] exact match in snippet view article find links to article

embedding. When there is an embedding, it can also be visualised as a subbundle of the Euclidean frame bundle E3 x SO(3), itself a submanifold of E3 x