Ricci curvature tensor of (K+1)-rulad surface in En.

Year 1988, Volume: 37 , - , 01.01.1988

Arif Sabuncuoğlu

https://doi.org/10.1501/Commua1_0000000551

Abstract

If we choose a natural companian basis (naturliche begleitbasis) for (k-|-l)-ruled surface in the Euclidean space E”, then the metric coefficients are ~ 1 < V, (t < k.
The Ricci curvature tensor S for a manifold is defined by S(X,Y) - L R (ep X, Y, e^.
n i.
In this paper we show that the Ricci curvature tensor of a (k-pl) - ruled surface in E'
S =
v,pt=‘
^i-ı
^ioR'^ov,] 0v 0 Ou.
ıs-
Here, -lOv} is the duaî hasis of the local cocrdinate hasis {evj-.

Keywords

Ricci curvature, tensor, surface in En.

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi