normal bundleの例文

• Suppose furthermore that there exists an isomorphism of normal bundles
• Then the isomorphism \ psi of normal bundles exists whenever their Euler classes are opposite:
• Since " E " is a smooth divisor, its normal bundle is a line bundle.
• The normal bundle associated with this ( stable class of ) embeddings is then the stable normal bundle.
• The normal bundle associated with this ( stable class of ) embeddings is then the stable normal bundle.
• This obstruction was stated ( in terms of the tangent bundle, not stable normal bundle ) by Whitney.
• The normal bundles of V in the two halves of the cut are opposite each other ( meaning symplectically anti-isomorphic ).
• The "'Weingarten equation "'is an analog of the Gauss formula for a connection in the normal bundle.
• Standard methods of algebraic geometry allow one to find the degree of a map by looking at an infinite fiber and its normal bundle.
• Assume furthermore that the weights of the isotropy representation of U ( 1 ) on the normal bundle N _ X Z are all 1.
• Thus, the cohomology dimension of the stable normal bundle, as detected by its highest non-vanishing characteristic class, is an obstruction to immersions.
• Surgery on normal maps allows one to systematically kill elements in the relative homotopy groups by representing them as embeddings " with trivial normal bundle ".
• Where each normal bundle N _ { M _ i } V is diffeomorphically identified with a neighborhood N _ i of V in M _ i, and the map
• More generally, one can formulate a similar trick using the normal bundle to define the Laplace Beltrami operator of any Riemannian manifold isometrically embedded as a hypersurface of Euclidean space.
• The resulting class of normal bundles ( it is a class of bundles and not a specific bundle because " N " could vary ) is called the stable normal bundle.
• The resulting class of normal bundles ( it is a class of bundles and not a specific bundle because " N " could vary ) is called the stable normal bundle.
• In many physical theories " E " is the tangent bundle, but for the fermions on the worldvolumes of D-branes in string theory it is a normal bundle.
• It can make it harder to imagine what a tangent vector might be, and there is no intrinsic notion of a normal bundle, but instead there is an intrinsic stable normal bundle.
• It can make it harder to imagine what a tangent vector might be, and there is no intrinsic notion of a normal bundle, but instead there is an intrinsic stable normal bundle.
• Further, codimenson 0 immersions do not behave like other immersions, which are largely determined by the stable normal bundle : in codimension 0 one has issues of fundamental class and cover spaces.