In the present Paper, the term „differential equations“ means systems of differential equations with partial derivatives. A uniform concept of geometry of differential equations does not exist in modern differential geometry. Representatives of different trends in geometry perceive geometry of differential equation in different ways. The theory of compatibility of differential equations and existence of solutions developed by Spenser-Goldsmidt is one of the most „geometrical“ among them. Later it was systematized and extended at the School of Moscow Mathematicians managed by A.Vinogradov (see [1]) and works of mathematicians from other countries [2].
Geometry of differential equations is also found in subjects of Lithuanian geometricians, first of all in investigations carried out by prof. V.Bliznikas and his disciples. The principal object of the said investigations was construction of internal bindings in differential equations.
The object of my Paper is an investigation on geometry of one class of systems of normal linear differential equations with partial derivatives. The said class of equations is presented by differential equations of the second order, provided in tangential stratifications of smooth manifolds.
Pursuing the said object, tensor fields are attributed to the differential equations under investigation in the internal manner and internal geometrical bindings of three kinds are developed. The developed bindings enable us to use their covariant... [to full text]
| Identifer | oai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2006~D_20060605_203749-37419 |
| Date | 05 June 2006 |
| Creators | Matvejenko, Ana |
| Contributors | Baliukonytė, Stasė, Sičiūnienė, Viktorija, Januškevičius, Romanas, Vosylius, Romualdas, Rutkauskas, Stasys, Vilnius Pedagogical University |
| Publisher | Lithuanian Academic Libraries Network (LABT), Vilnius Pedagogical University |
| Source Sets | Lithuanian ETD submission system |
| Language | Lithuanian |
| Detected Language | English |
| Type | Master thesis |
| Format | application/pdf |
| Source | http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060605_203749-37419 |
| Rights | Unrestricted |
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