affine bundle造句

• With respect to the affine bundle coordinates ( 2 ).
• For instance, the tangent bundle TX of a manifold X naturally is an affine bundle.
• (ii ) There is an affine bundle atlas of Y \ to X whose local trivializations morphisms and transition functions are affine isomorphisms.
• By a morphism of affine bundles is meant a bundle morphism \ Phi : Y \ to Y'whose restriction to each fiber of Y is an affine map.
• In particular, every vector bundle Y has a natural structure of an affine bundle due to these morphisms where s = 0 is the canonical zero-valued section of Y.
• With respect to affine bundle coordinates ( x ^ \ lambda, y ^ i ) on Y, an affine connection \ Gamma on Y \ to X is given by the tangent-valued connection form
• An affine bundle Y \ to X is a fiber bundle with a reducible to a general linear group GL ( m, \ mathbb R ), i . e ., an affine bundle admits an atlas with linear transition functions.
• An affine bundle Y \ to X is a fiber bundle with a reducible to a general linear group GL ( m, \ mathbb R ), i . e ., an affine bundle admits an atlas with linear transition functions.
• Being a vector bundle, the tangent bundle TX of an n-dimensional manifold X admits a natural structure of an affine bundle ATX, called the " affine tangent bundle ", possessing bundle atlases with affine transition functions.
• Every affine bundle morphism \ Phi : Y \ to Y'of an affine bundle Y modelled on a vector bundle \ overline Y to an affine bundle Y'modelled on a vector bundle \ overline Y'yields a unique linear bundle morphism
• Every affine bundle morphism \ Phi : Y \ to Y'of an affine bundle Y modelled on a vector bundle \ overline Y to an affine bundle Y'modelled on a vector bundle \ overline Y'yields a unique linear bundle morphism
• Every affine bundle morphism \ Phi : Y \ to Y'of an affine bundle Y modelled on a vector bundle \ overline Y to an affine bundle Y'modelled on a vector bundle \ overline Y'yields a unique linear bundle morphism