On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1

Görgülü, Ali; Ekici, Cumali

doi:10.3390/mca5020149

Open AccessArticle

On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1

by

Ali Görgülü

^* and

Cumali Ekici

Osmangazi University, Dept. of Mathematics, 26480 EskiFhir, Turkey

^*

Author to whom correspondence should be addressed.

Math. Comput. Appl. 2000, 5(3), 149-155; https://doi.org/10.3390/mca5020149

Published: 1 December 2000

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Abstract

If we choose a natural companion basis for \((k+1)\)-dimensional semi-ruled surfaces in semi-Euclidean space \(E_{\nu}^{n+1}\), then the metric coefficients are \(g_{ij} = \epsilon_{i}\delta_{ij}\), \(1\leq i\), \(j \leq k\). In this paper we show that the Ricci curvature tensor of a \((k+1)\)-dimensional semi-ruled surfaces in semi-Euclidean space \(E_{\nu}^{n+1}\) is \( S = \sum_{j,h=0}^{k}{\epsilon_{jh}} \left( \epsilon_{0} R_{h-j}^{0} g_{00} + \sum_{i=0}^{k}{R_{hij}^{i}} + \sum_{i=0}^{k}{g_{i0}} \left(\epsilon_{i} R_{hij} + \epsilon_{0} R_{h0j}^{i} \right)\right) \theta_{j} \otimes \theta_{h}. \) Here, \(\{\theta_{0}, \theta_{1}, ... \theta_{k}\}\) is the dual basis of the local coordinate basis \(\{e_{0} , e_{1} , ...e_{k}\}\).

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MDPI and ACS Style

Görgülü, A.; Ekici, C. On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1. Math. Comput. Appl. 2000, 5, 149-155. https://doi.org/10.3390/mca5020149

AMA Style

Görgülü A, Ekici C. On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1. Mathematical and Computational Applications. 2000; 5(3):149-155. https://doi.org/10.3390/mca5020149

Chicago/Turabian Style

Görgülü, Ali, and Cumali Ekici. 2000. "On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1" Mathematical and Computational Applications 5, no. 3: 149-155. https://doi.org/10.3390/mca5020149

APA Style

Görgülü, A., & Ekici, C. (2000). On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1. Mathematical and Computational Applications, 5(3), 149-155. https://doi.org/10.3390/mca5020149

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On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1

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