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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 prove a necessary and sufficient condition for a unique Einstein's connection to exist in $3$-dimensional ${}^*{g}-ESX_3$ and to display a surveyable tnesorial representation of $3$-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.
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참고문헌 (6)
참고문헌 신청
황인호 / 2014 / On the algebra of 3-dimensional ES-manifold / 한국수학논문집 22(1):207~216
Datta, D.k. / 1964 / Some theorems on symmetric recurrent tensors of the second order / Tensor 15:1105~1136
Einstein, A. / 1950 / The meaning of relativity / Princeton University Press
Mishra, R.S. / 1959 / n-dimensional considerations of uni ed eld theory of relativity / Tensor 9:217~225
Chung, K.T. / 1963 / Einstein's connection in terms of g / Nuovo cimento Soc. Ital. Fis. B 27(10):1297~1324
Datta, D.k. / 1964 / Some theorems on symmetric recurrent tensors of the second order / Tensor 15:1105~1136
Einstein, A. / 1950 / The meaning of relativity / Princeton University Press
Mishra, R.S. / 1959 / n-dimensional considerations of uni ed eld theory of relativity / Tensor 9:217~225
Chung, K.T. / 1963 / Einstein's connection in terms of g / Nuovo cimento Soc. Ital. Fis. B 27(10):1297~1324
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