Korean J. Math.  Vol 26, No 1 (2018)  pp.43-51
DOI: http://dx.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

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.

Keywords


ES-manifold, Recurrence relation, Einstein's connection

Subject classification

83E50, 83C05, 58A05

Sponsor(s)

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

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References


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