Korean J. Math.  Vol 26, No 1 (2018)  pp.43-51
DOI: https://doi.org/10.11568/kjm.2018.26.1.43

The study on the Einstein's connection in $5$-dimensional $ES$-manifold for the second class

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 derive a new set of powerful recurrence relations and to prove a necessary and sufficient condition for a unique Einstein's connection to exist in $5$-dimensional ${}^*{g}-ESX_5$ and to display a surveyable tnesorial representation of $5$-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the second class.


ES-manifold, Recurrence relation, Einstein's connection

Subject classification

83E50, 83C05, 58A05


This research was supported by Incheon National University Research Grant, 2017-2018.

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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)


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