| dc.contributor.author | Yue, Jin. | en_US |
| dc.date.accessioned | 2014-10-21T12:36:00Z | |
| dc.date.available | 2005 | |
| dc.date.issued | 2005 | en_US |
| dc.identifier.other | AAINR08405 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/54735 | |
| dc.description | The thesis is devoted to the development of certain aspects of the invariant theory of Killing tensors (ITKT) defined on pseudo-Riemannian spaces of constant curvature. A systematic study of ITKT began in 2001 by incorporating the underlying ideas of the classical invariant theory (CIT) of homogeneous polynomials into the geometric study of Killing tensors. One of the main problems in this study is the development of effective algorithms that can be used to determine the invariants, covariants and joint invariants. The methods of infinitesimal generators (which can be traced back to A. Cayley) and moving frames (as recently reformulated by P. Olver and others) have proven to be most effective in tackling this task. | en_US |
| dc.description | We begin by presenting comprehensive reviews of pseudo-Riemannian geometry and CIT that are blended together in ITKT. We review the notion of an isometry group invariant of Killing tensors and then, in complete analogy with the corresponding notions in CIT, introduce the new concepts of a covariant and a joint invariant of Killing tensors. We use the method of moving frames, in particular the inductive technique introduced by I. Kogan and used in the study of differential invariants, to compute fundamental invariants and covariants of certain vector spaces of Killing tensors. | en_US |
| dc.description | Our next goal is to formulate and prove an analogue of the result known in CIT as the 1856 lemma of Cayley. More specifically, we establish a Lie algebra representation of the isometry group on the vector space of Killing tensors of arbitrary valence defined on the Minkowski plane. The result is extended by solving the corresponding problem of the determination of a set of fundamental invariants. | en_US |
| dc.description | We apply these results to solve the problems of group invariant classification of the orthogonal coordinate webs generated by Killing two-tensors defined on the Euclidean and Minkowski planes. Our results compare well with the solutions obtained previously by other methods. In addition, we study the Drach potentials and show that the ten Killing tensors of valence three that define the corresponding first integrals cubic in the momenta are isometrically distinct. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 2005. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Development of the invariant theory of Killing tensors defined on pseudo-Riemannian spaces of constant curvature. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
