2 semiparallel surfaces in space forms I Two particular cases


Arslan K., Lumiste U., Murathan C., Özgür C.

PROCEEDINGS-ESTONIAN ACADEMY OF SCIENCES PHYSICS MATHEMATICS, vol.49, no.3, pp.139-148, 2000 (SCI-Expanded)

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.