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

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 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.

Keywords


ES-manifold, Einstein’s connection.

Subject classification

83E50, 83C05, 58A05.

Sponsor(s)

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

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References


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