A study on the recurrence relations of $5$-dimensional $ES$-manifold
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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 study the algebraic geometric structures of $5$-dimensional ${}^*{g}-ESX_5$. Particularly, in $5$-dimensional ${}^*{g}-ESX_5$, we derive a new set of 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 study the algebraic geometric structures of $5$-dimensional ${}^*{g}-ESX_5$. Particularly, in $5$-dimensional ${}^*{g}-ESX_5$, we derive a new set of powerful recurrence relations in the first class.
참고문헌 (5)
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- A. Einstein, "The meaning of relativity" (1950), Princeton University Press
- V. Hlavaty, "Geometry of Einstein's unified field theory" (1957), Noordhoop Ltd
- R.S. Mishra, "n-dimensional considerations of unified field theory of relativity", Tensor, 9, pp.217~225 (1959)