Parallel and semiparallel space-like submanifolds of low dimension in pseudo-Euclidean space
| dc.contributor.author | Safiulina, Elena | |
| dc.date.accessioned | 2013-11-19T09:06:08Z | |
| dc.date.available | 2013-11-19T09:06:08Z | |
| dc.date.issued | 2013-11-19 | |
| dc.description.abstract | Väitekirja uurimisvaldkonnaks on diferentsiaalgeomeetria. Ruumisarnast (Riemanni) alammuutkonda nimetatakse semiparalleelseks, kui kehtib suvaliste puutujavektorite X, Y korral. Siin on van der Waerdeni-Bortolotti seostuse kõverusoperaator ja h on teine fundamentaalvorm. Semiparalleelsete alammuutkondade klassis võib eraldada paralleelsete alammuutkondade alamklassi, kuhu kuuluvad alam-muutkonnad paralleelse teise fundamentaalvormiga h. Paralleelseid ja semiparalleelseid alammuutkondi eukleidilises ja konstantse kõverusega ruumis on uurinud mitmed matemaatikud (D. Ferus, J. Deprez, Ü. Lumiste). Käesoleva väitekirja uurimisobjektideks on paralleelsed ja semiparalleelsed ruumisarnased madala-mõõtmelised alammuutkonnad pseudoeukleidilises ruumis Semiparalleelsete alammuutkondade kirjelda-miseks kasutatakse asjaolu, et igaüks neist on paralleelsete alammuutkondade teist järku mähkija. | et |
| dc.description.abstract | The thesis is a study in differential geometry. A space-like (Riemannian) submanifold is called semi-parallel if (this is the integrability condition of the system h = 0 which characterizes a parallel submanifold. Here is the curvature operator of the van der Waerden-Bortolotti connection and h is the second fundamental form. Parallel and semiparallel submanifolds in the Euclidean space and in the space with a constant curvature have been studied by several mathematicians (e.g. D. Ferus, J. Deprez, Ü. Lumiste). In the present thesis the parallel and semiparallel space-like submanifolds of low dimension in pseudo-Euclidean space are derived. For description of semiparallel submanifolds is used result that every of them is a second order envelope of a family of corresponding parallel submanifolds. | en |
| dc.identifier.isbn | 978-9949-32-443-9 (print) | |
| dc.identifier.isbn | 978-9949-32-444-6 (pdf) | |
| dc.identifier.issn | 1024-4212 | |
| dc.identifier.uri | http://hdl.handle.net/10062/34564 | |
| dc.language.iso | en | et |
| dc.relation.ispartofseries | Dissertationes mathematicae Universitatis Tartuensis;89 | |
| dc.subject.other | dissertatsioonid | et |
| dc.subject.other | ETD | en |
| dc.subject.other | dissertations | en |
| dc.subject.other | väitekirjad | et |
| dc.title | Parallel and semiparallel space-like submanifolds of low dimension in pseudo-Euclidean space | en |
| dc.title.alternative | Paralleelsed ja semiparalleelsed ruumisarnased madalamõõtmelised alammuutkonnad pseudoeukleidilises ruumis | et |
| dc.type | Thesis | en |