Korean J. Math.  Vol 23, No 2 (2015)  pp.313-321
DOI: https://doi.org/10.11568/kjm.2015.23.2.313

Einstein's connection in $3$-dimensional $ES$-manifold

In Ho Hwang


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 prove a necessary and sufficient condition for a unique Einstein's connection to exist in $3$-dimensional ${}^*{g}-ESX_3$ and to display a surveyable tnesorial representation of $3$-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.


ES-manifold, Einstein’s connection.

Subject classification

83E50, 83C05, 58A05.


This research was supported by Incheon National University Research Grant, 2013-2014.

Full Text:



Hwang, I.H., On the algebra of 3-dimensional ES-manifold , Korean J. Math. 22 (1) (2014), 207–216. (Google Scholar)

Datta, D.k., Some theorems on symmetric recurrent tensors of the second order, Tensor (N.S.) 15 (1964), 1105–1136. (Google Scholar)

Einstein, A., The meaning of relativity, Princeton University Press, 1950. (Google Scholar)

Mishra, R.S., n-dimensional considerations of unified field theory of relativity, Tensor 9 (1959), 217–225. (Google Scholar)

Chung, K.T., Einstein’s connection in terms of ∗gλν, Nuovo cimento Soc. Ital. Fis. B, 27 (1963), (X), 1297–1324 (Google Scholar)

Hlavaty ́, V., Geometry of Einstein’s unified field theory, Noordhoop Ltd., 1957 (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr