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Obstructions to conformally Einstein metrics in \(n\) dimensions. (English) Zbl 1098.53014

The authors present invariant polynomials in the Riemannian curvature and its covariant derivatives whose vanishing characterizes for a particular class of metrics those metrics which are locally conformally Einstein. These results generalize the work by C. N. Kozameh, E. T. Newman and K. P. Tod [Gen. Relativ. Gravitation 17, 343–352 (1985; Zbl 0564.53011)] in dimension four and by M. Listing [Ann. Global Anal. Geom. 20, 183–197 (2001; Zbl 1024.53031)] in arbitrary dimension. One can also characterize metrics which are locally conformally Einstein as metrics for which the standard tractor bundle admits a suitable generic parallel section.

MSC:

53B20 Local Riemannian geometry
53A30 Conformal differential geometry (MSC2010)
53B15 Other connections
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References:

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