Notes on conformal differential geometry
Notes on conformal differential geometry
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共形微分几何的注释
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
M. Eastwood
中科院分区：
文献类型：
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作者：
M. Eastwood
这篇综述论文介绍了一系列的四个讲座的讲义，它提供了一个介绍共形微分几何的几个主题。特别是，一个非常好的和温和的介绍共形黎曼结构本身，平坦或弯曲，是在开始。然后，协变导数下的度量的重新标度的行为进行了描述。这导致了彭罗斯的局部扭矢输运，该输运是在T. Y.托马斯。由此产生的对象被称为拖拉机连接，等价于广义空间上的嘉当连接概念[参见T。N.贝利，M。G.伊斯特伍德和R。A. Gover}，Rocky Mt. 24，1191-1217（1994; Zbl 0828.53012）]。\par第三次讲座建立明确的联系，表示理论，并介绍了不变的运营商在齐次向量丛的圆形球（的！
This survey paper presents lecture notes from a series of four lectures addressed to a wide audience and it offers an introduction to several topics in conformal differential geometry. In particular, a very nice and gentle introduction to the conformal Riemannian structures themselves, flat or curved, is presented in the beginning. Then the behavior of the covariant derivatives under the rescaling of the metrics is described. This leads to Penrose's local twistor transport which is introduced in the approach credited to T. Y. Thomas. The resulting object is called the tractor connection and is equivalent to Cartan's concept of connections on generalized spaces [see also {\it T. N. Bailey, M. G. Eastwood} and {\it R. A. Gover}, Rocky Mt. J. Math. 24, 1191-1217 (1994; Zbl 0828.53012)]. \par The third lecture builds explicit links to the representation theory and describes the invariant operators on the homogeneous vector bundles over the round sphere (the homogeneou!