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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.
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참고문헌 (5)
참고문헌 신청
Datta, D.k / 1964 / Some theorems on symmetric recurrent tensors of the second order / Tensor (N.S.) 15:1105~1136
Einstein, A. / 1950 / The meaning of relativity / Princeton University Press
Mishra, R.S. / 1959 / n-dimensional considerations of unified field theory of relativity / Tensor 9:217~225
Chung, K.T. / 1963 / Einstein's connection in terms of $^{\ast}g^{{\lambda}{\nu}}$ / Nuovo cimento Soc. Ital. Fis. B 27:1297~1324
Hlavaty, V. / 1957 / Geometry of Einstein's unified field theory / Noordhoop Ltd
Einstein, A. / 1950 / The meaning of relativity / Princeton University Press
Mishra, R.S. / 1959 / n-dimensional considerations of unified field theory of relativity / Tensor 9:217~225
Chung, K.T. / 1963 / Einstein's connection in terms of
Hlavaty, V. / 1957 / Geometry of Einstein's unified field theory / Noordhoop Ltd
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