Supervisor: Ülo Lumiste, TÜ, matemaatika instituut
DSc, Prof. Vanya Mirzoyan Armeenia Riiklik Tehnikalikool Jerevan, Armeenia Vabariik
Cand. Sc., Assoc. Prof. Emer. Kaarin Riives-Kaagjärv Eesti Maalikool
The thesis is a study in differential geometry. A space-like (Riemannian) submanifold Mm is called semiparallel if R(X, Y )h = 0 (this is the integrability condition of the system ∇h = 0 which charac- terizes a parallel submanifold. Here R 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 mathe- maticians(e.g.D.Ferus,J.Deprez,U ̈.Lumiste).Inthepresentthesistheparallelandsemiparallel space-like submanifolds of low dimension in pseudo-Euclidean space Esn 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.