Einstein's connection in $3$-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 $3$-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.
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 $3$-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.
참고문헌 (6)
- 황인호, "On the algebra of 3-dimensional ES-manifold", 한국수학논문집, 22(1), pp.207~216 (2014), 강원경기수학회[DOI]
- Datta, D.k., "Some theorems on symmetric recurrent tensors of the second order", Tensor, 15, pp.1105~1136 (1964)
- Einstein, A., "The meaning of relativity" (1950), Princeton University Press
- Mishra, R.S., "n-dimensional considerations of uni ed eld theory of relativity", Tensor, 9, pp.217~225 (1959)
- Chung, K.T., "Einstein's connection in terms of g", Nuovo cimento Soc. Ital. Fis. B, 27(10), pp.1297~1324 (1963)
- Hlavaty, V., "Geometry of Einstein's uni ed eld theory" (1957), Noordhoop Ltd.