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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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TL;DR: In this paper, stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions.
Abstract: Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua.
118 citations
TL;DR: In this article, the authors studied the quantum sphere as a quantum Riemannian manifold in the quantum frame bundle approach and exhibited its 2-dimensional cotangent bundle as a direct sum Ω 0,1⊕Ω 1,0 in a double complex.
Abstract: We study the quantum sphere Open image in new window as a quantum Riemannian manifold in the quantum frame bundle approach We exhibit its 2-dimensional cotangent bundle as a direct sum Ω0,1⊕Ω1,0 in a double complex We find the natural metric, volume form, Hodge * operator, Laplace and Maxwell operators and projective module structure We show that the q-monopole as spin connection induces a natural Levi-Civita type connection and find its Ricci curvature and q-Dirac operator Open image in new window We find the possibility of an antisymmetric volume form quantum correction to the Ricci curvature and Lichnerowicz-type formulae for Open image in new window We also remark on the geometric q-Borel-Weil-Bott construction
113 citations
TL;DR: In this article, the right-hand side of the integral of t/(M) for hyperbolic 3-manifolds is calculated explicitly, in a special case, for Riemannian manifolds of dimension 3.
Abstract: In this paper, we use the formula in the above theorem to study t/(M) for hyperbolic 3-manifolds and calculate the right-hand side of the formula explicitly, in a special case. Our main task is to represent the integral of/]1 by some more tractible ones. In Sect. 1, we deal with general compact oriented Riemannian manifolds M of dimension 3. Let F(M) be the SO(3) oriented frame bundle of M. Let L be a
109 citations
TL;DR: In this article, the vector bundle moduli superpotential for a vector bundle with structure group G=SU(3), generated by a heterotic superstring wrapped once over an isolated curve in a Calabi-Yau threefold with base B=F1, is explicitly calculated.
108 citations
TL;DR: In this article, the existence of a meromorphic reduction map is shown to be almost holomorphic, i.e. the reduction map has compact fibers which do not meet the indeterminacy locus of the reduction maps.
Abstract: In [Ts00], H. Tsuji stated several very interesting assertions on the structure of pseudo-effective line bundles L on a projective manifold X. In particular he postulated the existence of a meromorphic “reduction map”, which essentially says that through the general point of X there is a maximal irreducible L-flat subvariety. Moreover the reduction map should be almost holomorphic, i.e. has compact fibers which do not meet the indeterminacy locus of the reduction map. The proofs of [Ts00], however, are extremely difficult to follow.
105 citations