共查询到20条相似文献,搜索用时 328 毫秒
1.
Anthony D. Blaom 《Transactions of the American Mathematical Society》2006,358(8):3651-3671
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie algebroid structure. The curvature of this connection vanishes precisely when the structure is locally symmetric.
This model generalizes Cartan geometries, a substantial class, to the intransitive case. Simple examples are surveyed and corresponding local obstructions to symmetry are identified. These examples include foliations, Riemannian structures, infinitesimal -structures, symplectic and Poisson structures.
2.
Grabowska Katarzyna Grabowski Janusz Urbaski Pawe 《Annals of Global Analysis and Geometry》2003,24(2):101-130
Natural affine analogs of Lie brackets on affine bundles are studied.In particular, a close relation to Lie algebroids and a duality withcertain affine analog of Poisson structure is established as well asaffine versions of complete lifts and Cartan exterior calculi. 相似文献
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In dimension 2, we give a local characterization of Levi-Civita connections, improving a result by G. Thompson (1991), and of Newton–Cartan connections (connections which are limit of Levi-Civita connections). 相似文献
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E. M. Romanova 《Russian Mathematics (Iz VUZ)》2009,53(5):59-62
We consider the quotient manifold of the manifold of nondegenerate affinor fields on a compact manifold with respect to the action of the group of nowhere vanishing functions. On this manifold, we construct a Cartan connection and find its torsion tensor. We also find the geodesics of the Cartan connection. 相似文献
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E. M. Romanova 《Russian Mathematics (Iz VUZ)》2008,52(7):33-37
We consider the quotient set of the set of nondegenerate affinor fields with respect to the action of the group of nowhere vanishing functions. This set is endowed with a structure of infinite-dimensional Lie group. On this Lie group, we construct an object of linear connection with respect to which all left-invariant vector fields are covariantly constant (the Cartan connection). 相似文献
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利用Chern联络D、Cartan张量A以及第二基本形式H.研究了Finsler子流形中的诱导Chern联络与第一、第二曲率R和P,给出了子流形的关于R曲率、P曲率以及flag曲率的Gauss方程。 相似文献
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Rui Loja Fernandes 《Advances in Mathematics》2002,170(1):119-179
We extend the notion of connection in order to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of a covariant connection. It allows us to define holonomy of the orbit foliation of a Lie algebroid and prove a Stability Theorem. We also introduce secondary or exotic characteristic classes, thus providing invariants which generalize the modular class of a Lie algebroid. 相似文献
9.
N. A. Kuz’mina 《Russian Mathematics (Iz VUZ)》2008,52(7):61-65
The paper is devoted to the study of intrinsic geometry of a Cartan distribution \(\mathcal{M}\) in projective space P2m . We essentially use the hyperband distribution \(\mathcal{H}\) and P2m associated with \(\mathcal{M}\). Using the duality theory, we construct, in the 4th differential neighborhood, a series of normalizations of \(\mathcal{M}\). We also consider dual affine connections \(\mathop \nabla \limits^1 \) and \(\mathop \nabla \limits^2 \) induced by the dual normalization of the Cartan distribution \(\mathcal{M}\). 相似文献
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We show how some basic dynamical ideas can be brought to bear on the study of Cartan geometries. In our main results, we give conditions for certain types of Cartan geometries to have constant curvature. We also consider ergodic actions of `higher-rank' semisimple groups on bundles supporting (not necessarily invariant) Cartan connections and show that these are `standard locally homogeneous' actions provided that some noncompact 1-parameter subgroup `preserves' a Cartan geometry. 相似文献
12.
Six classes of Riemann—Cartan manifolds are distinguished in an invariant way. Geometric characteristics of some of the distinguished classes of Riemann—Cartan manifolds are found, and also conditions hindering the existence, are determined. The local geometry of Riemann—Cartan manifolds carrying pseudo-Killing and pseudoharmonic vector fields is studied. Conditions hindering the existence “in the large” of pseudo-Killing and pseudoharmonic vector fields on Riemann—Cartan manifolds are obtained. 相似文献
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Jens Carsten Jantzen 《Mathematische Zeitschrift》2013,275(1-2):569-594
Consider a finite dimensional restricted Lie algebra over a field of prime characteristic. Each linear form on this Lie algebra defines a finite dimensional quotient of its universal enveloping algebra, called a reduced enveloping algebra. This leads to a Cartan matrix recording the multiplicities as composition factors of the simple modules in the projective indecomposable modules for such a reduced enveloping algebra. In this paper we show how to compare such Cartan matrices belonging to distinct linear forms. As an application we rederive and generalise the reciprocity formula first discovered by Humphreys for Lie algebras of reductive groups. For simple Lie algebras of Cartan type we see, for example, that the Cartan matrices for linear forms of non-positive height are submatrices of the Cartan matrix for the zero linear form. 相似文献
16.
In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures. 相似文献
17.
Yu. B. Ermolayev 《Russian Mathematics (Iz VUZ)》2008,52(10):1-12
We revise the notion of a Cartan extension and consider in detail simple examples of known Cartan extensions. 相似文献
18.
Sorin Dumitrescu 《Monatshefte für Mathematik》2010,19(2):145-154
We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi–Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus. 相似文献
19.
E. Mazėtis 《Lithuanian Mathematical Journal》2000,40(2):148-155
Cartan spaces equipped with almost complex and almost antiquaternion structures are considered. The Hermitian metrics of almost complex Cartan spaces are found. It is proved that in the Cartan spaces there always exist Kählerian metrics. The conditions of the complete integrability of these structures are established, and the method of constructing affine connections consistent with these structures is given. 相似文献
20.
The third author recently proved that the Shoikhet–Dolgushev L∞-morphism from Hochschild chains of the algebra of smooth functions on a manifold to differential forms extends to cyclic chains. Localization at a solution of the Maurer–Cartan equation gives an isomorphism, which we call character map, from the periodic cyclic homology of a formal associative deformation of the algebra of functions to de Rham cohomology. We prove that the character map is compatible with the Gauss–Manin connection, extending a result of Calaque and Rossi on the compatibility with the cap product. As a consequence, the image of the periodic cyclic cycle 1 is independent of the deformation parameter and we compute it to be the A-roof genus of the manifold. Our results also imply the Tamarkin–Tsygan index theorem. 相似文献