Recently I became aware of ‘The Holonomy Group’. This is to do with how the components of vectors alter, upon their parallel transport in a Riemann space.
There are six papers on ‘The Holonomy Group’, by V.Hlavaty, that are all available on JSTOR. These papers are References 1-6.
For anyone interested in these six papers, I suggest starting with a first brief look at Reference 2, pg. 12, see (4.1).
I wonder if these papers are relevant to current research in ‘General Relativity’?
I would like to obtain an understanding of what’s going on in Reference 1.
My actual question is: Could anyone provide a summary, of what’s going on in these six papers?
References:
1, HLAVATÝ, VÁCLAV. “The Holonomy Group I. The Curvature Tensor.” Journal of Mathematics and Mechanics, vol. 8, no. 2, 1959, pp. 285–307. JSTOR, http://www.jstor.org/stable/24900561 . Accessed 22 Aug. 2022.
2, HLAVATÝ, V. “The Holonomy Group II. The Lie Group Induced by a Tensor.” Journal of Mathematics and Mechanics, vol. 8, no. 4, 1959, pp. 597–622. JSTOR, http://www.jstor.org/stable/24900677. Accessed 22 Aug. 2022.
3, HLAVATÝ, VÁCLAV. “The Holonomy Group III. Metrisable Spaces.” Journal of Mathematics and Mechanics, vol. 9, no. 1, 1960, pp. 89–122. JSTOR, http://www.jstor.org/stable/24900513. Accessed 22 Aug. 2022.
4, HLAVATÝ, VÁCLAV. “The Holonomy Group IV. The General Ln with Symmetric Connection.” Journal of Mathematics and Mechanics, vol. 9, no. 3, 1960, pp. 453–96. JSTOR, http://www.jstor.org/stable/24900484. Accessed 22 Aug. 2022.
5, HLAVATÝ, VÁCLAV. “The Holonomy Group V. Weyl Space W 4 , First Part.” Journal of Mathematics and Mechanics, vol. 10, no. 2, 1961, pp. 317–48. JSTOR, http://www.jstor.org/stable/24900828. Accessed 22 Aug. 2022.
6, HLAVATÝ, V. “The Holonomy Group VI. Weyl Space W 4 , Second Part.” Journal of Mathematics and Mechanics, vol. 11, no. 1, 1962, pp. 35–59. JSTOR, http://www.jstor.org/stable/24900845. Accessed 22 Aug. 2022.
You can find a summary at https://en.wikipedia.org/wiki/Holonomy
Inclusive Riemannian homology (scroll down).
With kind regards, Sydney
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