Let $M$ be a vector bundle over $X-D$ equipped with a flat connection with possible irregular singularities along $D$. We define a cleanliness condition which roughly says that the singularities of the connection are controlled by the singularities at the generic points of $D$. When this ...
flat complex vector bundle的所有chern类都是平凡的吗？若 [公式] 是一个flat complex vector bundle，...
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We construct an irreducible holomorphic connection with SL(2,R)–monodromy on the trivial holomorphic vector bundle of rank two over a compact Riemann surface. This answers a question of Calsamiglia, Deroin, Heu and Loray in [5]. Résumé Dans cet article nous munissons le fibré vectoriel...
by E = G × H/Γ with Γ acting on G by deck transformations and on H via ρ. Such a bundle admits a trivialization compatible with the flat connection if and only if the representation is trivial. However, we will be concerned whether there exists ...
Letbe the eigenvalues of the Laplace–Beltrami operator on,be the eigenvalues of the connection Laplacian on divergence-free 1-forms onandbe the eigenvalues of the Einstein operator on transverse and traceless tensors on. (i) The indicial set of the Lichnerowicz Laplacianonis given by ...
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We describe two extensions of the notion of a self-dual connection in a vector bundle over a manifold M from dim M=4 to higher dimensions. The first extension, Omega-self-duality, is based on the existence of an appropriate 4-form Omega on the Riemannian manifold M and yields solutions ...
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manifold if the holonomy group of its Levi-Civita connection of g lies inside of G 2 ⊂ SO(7). A G 2 manifold is equipped with a vector cross product × on its tangent bundle and a harmonic (calibration) 3-form ϕ ∈ Ω ...