On the algebra of 3-dimensional ES-manifold
Main Article Content
Abstract
The manifold $ {}^*{g} - ESX_n $ is a generalized $ n $-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $ {}^*{g}^{ \lambda \nu } $ through the $ ES $-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of $3$-dimensional ${}^*{g}-ESX_3$. Particularly, in $3$-dimensional ${}^*{g}-ESX_3$, we derive a new set of powerful recurrence relations in the first class.
Article Details
Supporting Agencies
This research was supported by Incheon National University Research Grant
2012-2013.
References
[1] Hwang, I.H., A study on the geometry of 2-dimensional RE-manifold X2, J. Korean Math. Soc. 32 (2) (1995), 301–309. Google Scholar
[2] Chung, K.T., Einstein’s connection in terms of ∗gλν, Nuovo cimento Soc. Ital. Fis. B 27 (1963), 1297–1324. Google Scholar
[3] Datta, D.k., Some theorems on symmetric recurrent tensors of the second order, Tensor (N.S.) 15 (1964), 1105–1136. Google Scholar
[4] Einstein, A., The meaning of relativity, Princeton University Press, 1950. Google Scholar
[5] Hlavaty , V., Geometry of Einstein's unified field theory, Noordhoop Ltd., 1957. Google Scholar
[6] Mishra, R.S., n-dimensional considerations of unified field theory of relativity, Tensor 9 (1959), 217–225. Google Scholar