Title of article :
H-Recurrent Surfaces in Euclidean Space E^m
Author/Authors :
Arslan, Kadri Uludag University - Department of Mathematics, Turkey , Murathan, Cengizhan Uludag University - Department of Mathematics, Turkey , Ozturk, Gunay Kocaeli University - Department of Mathematics, Turkey , Turkay, Selen Columbia University - Science and Technology Teachers College - Department of Mathematics, USA
Abstract :
The object of the paper is to study some smooth surfaces M whose mean curvature vector H satisfies the H-recurrent condition DX H = λ(X)H in m-dimensional Euclidean space E^m, where X is a tangent vector field of M and λ is a 1-form. First of all,we prove that the surfaces which satisfy the Hrecurrent condition in Em are R⊥-parallel (i.e., R⊥H = 0). Then, we show that H-parallel surfaces in E^5 are either totally umbilical or normally flat.
Keywords :
Mean curvature vector , H , parallel surfaces
Journal title :
Selcuk Journal of Applied Mathematics
Journal title :
Selcuk Journal of Applied Mathematics
