Korean J. Math. Vol. 25 No. 1 (2017) pp.127-135
DOI: https://doi.org/10.11568/kjm.2017.25.1.127

Einstein's connection in $5$-dimensional $ES$-manifold

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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 $5$-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 first class.

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