In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics


Volume 49 No. 3 September 2000


2-Semiparallel surfaces in space forms. 1. Two particular cases; 139–148

Kadri ARSLAN, Ülo LUMISTE, Cengizhan MURATHAN, and Cihan ÖZGÜR

Abstract. 2-Semiparallel surfaces are introduced as surfaces satisfying the integrability condition of the differential system, which characterizes the 2-parallel surfaces, i.e. such surfaces whose third fundamental form  is parallel. The latter have been classified by the second author. Now our aim is to classify the 2-semiparallel surfaces in space forms. As the first step this is done for two particular cases. It is shown that for these cases, in addition to surfaces with flat  only those surfaces can occur which are either parallel (i.e. with  or have vanishing Gaussian curvature (i.e. flat  with some additional condition.

Key words: parallel surfaces, semiparallel surfaces, 2-semiparallel surfaces.


Parallel and semiparallel symplectic submanifolds in the symplectic space; 149–169


Abstract. Parallel and semiparallel symplectic submanifolds in the symplectic space are considered. It is proved that in this space some results are analogical to the results in the Euclidean space.

Key words: symplectic space, parallel and semiparallel symplectic submanifolds, moving frame.


Tauberian theorems for generalized summability methods in Banach spaces; 170–182


Abstract. Tauberian theorems (T-theorems) for different generalized summability methods A = (Ank) and sequences of points in Banach spaces X are proved by a universal method. The operators Ank : X ® X  are continuous and linear on X. T-theorems with o-conditions for generalized Riesz and Euler–Knopp methods of cX®cX type are presented (cX being the space of convergent X-valued sequences). The applications of general results to scalar matrix methods are discussed. Several classical T-theorems arise from the results of the study as conclusions.

Key words: Banach spaces, operators, generalized summability methods, Tauberian theorems, Tauberian conditions, Mercer's theorems.


Tauberian remainder theorems for two families of summability methods; 183–189


Abstract. Some Tauberian remainder theorems are proved for two families of triangular matrix methods. Using these theorems, several special cases are studied. The discussed method gives an additional way to get Tauberian remainder theorems for some normal methods of summability not belonging to these families, but which are close to these families in some respect.

Key words: Tauberian remainder theorems.




Juhan Ross 75; 190–192

Endel Lippmaa 70; 193–195