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Invariants of four-dimensional Riemannian spaces and their varying under conformal transformation. (Russian) Zbl 0932.53013
The invariants of four-dimensional Lorentzian space were studied in a number of papers [see, e.g., P. I. Petrov, Dokl. Akad. Nauk SSSR 113, 1214-1217 (1957; Zbl 0079.38102); A. P. Norden and V. V. Vishnevskij, Izv. Vyssh. Zaved., Mat. 1959, No. 2(9), 176-182 (1959; Zbl 0114.37502); etc.].
In the present paper, the varying of the invariants of four-dimensional Riemannian space of arbitrary signature under conformal transformation is found in an explicit form. The author also presents an algorithm for computer calculations and the corresponding program written with the use of Reduce.
MSC:
53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53-04 Software, source code, etc. for problems pertaining to differential geometry
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