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searching for Dual bundle 5 found (19 total)

Smooth scheme (1,047 words) [view diff] exact match in snippet view article find links to article

The tangent bundle of a smooth scheme over k can be defined as the dual bundle, TX = (Ω1)*. Smoothness is a geometric property, meaning that for any

Connection (vector bundle) (8,674 words) [view diff] exact match in snippet view article

∈ Γ ( E ∗ ) {\displaystyle \xi \in \Gamma (E^{*})} a section of the dual bundle, and ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } the natural

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

one-dimensional space, denoted by O(H), and called the hyperplane bundle. The dual bundle is denoted O(−H), and the kth tensor power of O(H) is denoted by O(kH)

Hamiltonian mechanics (9,323 words) [view diff] exact match in snippet view article find links to article

fiberwise Legendre transform of the Lagrangian produces a function on the dual bundle over time whose fiber at t is the cotangent space T∗Et, which comes equipped

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

Then the tangent bundle T X {\displaystyle TX} is defined to be the dual bundle ( Ω 1 ) ∗ {\displaystyle (\Omega ^{1})^{*}} . For X {\displaystyle X}