EINSTEIN'S CONNECTION IN 5-DIMENSIONAL ES-MANIFOLD
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초록
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.
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.
참고문헌 (6)
- 황인호, "A study on the recurrence relations of $5$-dimensional $ES$-manifold", 한국수학논문집, 24(3), pp.319~330 (2016), 강원경기수학회[DOI]
- D.k. Datta, "Some theorems on symmetric recurrent tensors of the second order", Tensor (N.S.), 15, pp.1105~1136 (1964)
- Einstein, A., "The meaning of relativity" (1950), Princeton University Press
- R.S. Mishra, "n-dimensional considerations of uni ed eld theory of relativity", Tensor, 9, pp.217~225 (1959)
- K.T. Chung, "Einstein's connection in terms of g", Nuovo cimento Soc. Ital. Fis. B, 27(10), pp.1297~1324 (1963)
- V. Hlavaty, "Geometry of Einstein's unified field theory" (1957), Noordhoop Ltd