Abstract
AbstractWe consider invariant covariant derivatives on reductive homogeneous spaces corresponding to the well-known invariant affine connections. These invariant covariant derivatives are expressed in terms of horizontally lifted vector fields on the Lie group. This point of view allows for a characterization of parallel vector fields along curves. Moreover, metric invariant covariant derivatives on a reductive homogeneous space equipped with an invariant pseudo-Riemannian metric are characterized. As a by-product, a new proof for the existence of invariant covariant derivatives on reductive homogeneous spaces and their the one-to-one correspondence to certain bilinear maps is obtained.
Funder
Bundesministerium für Bildung und Forschung
Julius-Maximilians-Universität Würzburg
Publisher
Springer Science and Business Media LLC
Reference18 articles.
1. Nomizu, K.: Invariant affine connections on homogeneous spaces. Am. J. Math. 76, 33–65 (1954). https://doi.org/10.2307/2372398
2. Jurdjevic, V., Markina, I., Silva Leite, F.: Symmetric spaces rolling on flat spaces. J. Geom. Anal. 33(3), 94–33 (2023). https://doi.org/10.1007/s12220-022-01179-5
3. Rabenoro, D., Pennec, X.: The geometry of Riemannian submersions from compact Lie groups. Application to flag manifolds. arXiV Preprint (2023). arXiv:2302.14810
4. Xu, M.: Submersion and homogeneous spray geometry. J. Geom. Anal. 32(6), 172–43 (2022). https://doi.org/10.1007/s12220-022-00911-5
5. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, vol. 60, p. 462. Springer, New York. Translated from the Russian by K. Vogtmann and A. Weinstein (1978)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Rolling reductive homogeneous spaces;Analysis and Mathematical Physics;2024-03-26