Geroch, Robert Multipole moments. I: Flat space. (English) Zbl 1107.83313 J. Math. Phys. 11, 1955-1961 (1970). Summary: There is an intimate connection between multipole moments and the conformal group. While this connection is not emphasized in the usual formulation of moments, it provides the starting point for a consideration of multipole moments in curved space. As a preliminary step in defining multipole moments in general relativity (a program which will be carried out in a subsequent paper), the moments of a solution of Laplace’s equation in flat 3-space are studied from the standpoint of the conformal group. The moments emerge as certain multilinear mappings on the space of conformal Killing vectors. These mappings are re-expressed as a collection of tensor fields, which then turn out to be conformal Killing tensors (first integrals of the equation for null geodesics). The standard properties of multipole moments are seen to arise naturally from the algebraic structure of the conformal group. Cited in 1 ReviewCited in 45 Documents MSC: 83C99 General relativity 53C80 Applications of global differential geometry to the sciences × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1007/BF01645486 · doi:10.1007/BF01645486 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.