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

Main Article Content

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 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.


Article Details

Supporting Agencies

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

References

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