Third-order tensor potentials for the Riemann and Weyl tensors. II: Singular solutions |
| |
Authors: | Franco Bampi Giacomo Caviglia |
| |
Affiliation: | (1) Institute of Engineering Mathematics, Pl Kennedy, 16129 Genova, Italy;(2) Institute of Mathematics, Via L. B. Alberti 4, 16132 Genova, Italy |
| |
Abstract: | The analysis of the admissibility of a potential representation for the Riemann tensor is here continued. As in the preceding paper, the starting point is to regard the relationship between the Riemann tensor and its possible potential as a system of partial differential equations determining the unknown potential. The first result, strengthening a previous conclusion, is that there never exist ordinary solutions. Surprisingly enough, in a four-dimensional Riemannian manifold the existence of singular solutions is established without requiring any integrability condition. Possible applications and generalizations are also suggested. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|