CONTENTS &
ABSTRACTS

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

Aivo PARRING

**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

Tamara SÕRMUS

**Abstract.** Tauberian theorems
(T-theorems) for different generalized summability methods *A* = (*A _{nk}*)
and sequences of points in Banach spaces

**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

Ivar TAMMERAID

**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.

CHRONICLE

Juhan Ross 75; 190–192

Endel Lippmaa 70; 193–195