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Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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26 citations
26 citations
TL;DR: Theorem 4.2 as discussed by the authors states that the smooth projective family of curves is invariant to a change in the base of the curve family, i.e., the bresofthe family are invariant.
Abstract: MathematicsSubjectClassi cation(1991):14J10,14D99Itisawell-knownconsequenceoftheTorellitheoremthatasmoothprojec-tivefamilyofcurvesofgenusatleast2overaprojectiverationalorellipticcurveisisotrivial,thatis,the bresofthefamilyareisomorphic.Sincetheautomorphismgroupofacurveofgenusatleast2is nite,thisalsoimpliesthatthefamilybecomestrivialaftera nitebasechange.The above statement was generalized for smooth projective families ofminimalsurfacesofgeneraltypein[Migliorini95],andforsmoothprojec-tivefamiliesofvarieties(ofarbitrarydimension)withamplecanonicalbundlein[Kovacs96].Botharticlesstudiedfamiliesovercurves.Theaimofthisarticleistopresentafurthergeneralization,namelyletthebaseofthefamilyhavearbitrarydimension.0.1Theorem=4.2Theorem.Letf:X !S beasmoothmorphismofpro-jectivealgebraicvarietiessuchthatthecanonicalbundleofevery breoffisample.AssumethatS isbirationaltoanS
26 citations
TL;DR: In this paper, a line bundle over the Brownian bridge is defined by using its section, which allows us to define a Hilbert space of spinor fields over the bridge when the first Pontryaguin class of the spin bundle is equal to 0.
Abstract: We give the definition of a line bundle over the Brownian bridge by using its section. This allows us to define a Hilbert space of sections of a line bundle over the Brownian bridge associated to the transgression of a representative of an element of H3(M;Z). We consider the case of a string structure over the Brownian bridge: this allows us to define a Hilbert space of spinor fields over the Brownian bridge, when the first Pontryaguin class of the spin bundle over the manifold is equal to 0.
25 citations
TL;DR: In this paper, the authors describe the composition of two product-preserving bundle functors on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps.
Abstract: Using the theory of Weil algebras, we describe the composition of two product preserving bundle functors on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. Then we deduce certain interesting geometric properties of the natural transformations of some of the iterated functors.
25 citations