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

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 $5$-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.


Keywords


ES-manifold, Einstein's connection

Subject classification

83E50, 83C05, 58A05

Sponsor(s)

INCHEON NATIONAL UNIVERSITY

Full Text:

PDF

References


I.H. Hwang, A study on the recurrence relations of 5-dimensional ES-manifold, Korean J. Math. 24 (3) (2016), 319–330. (Google Scholar)

D.k. Datta, Some theorems on symmetric recurrent tensors of the second order, Tensor (N.S.) 15 (1964), 1105–1136. (Google Scholar)

A. Einstein, The meaning of relativity, Princeton University Press, 1950. (Google Scholar)

R.S. Mishra, n-dimensional considerations of unified field theory of relativity, Tensor 9 (1959), 217–225. (Google Scholar)

K.T. Chung, Einstein’s connection in terms of ∗gλν, Nuovo cimento Soc. Ital. Fis. B 27 (1963), (X), 1297–1324 (Google Scholar)

V. Hlavaty ́, Geometry of Einstein’s unified field theory, Noordhoop Ltd., 1957. (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr