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On the algebra of 3-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 3-dimensional *g-ESX_3. Particularly, in 3-dimensional *g-ESX_3, 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 3-dimensional *g-ESX_3. Particularly, in 3-dimensional *g-ESX_3, we derive a new set of powerful recurrence relations in the first class.

참고문헌 (6)

  1. Hwang, I.H., "A study on the geometry of 2-dimensional RE-manifold X2X2", J. Korean Math. Soc, 32(2), pp.301~309 (1995)
  2. Chung, K.T., "Einstein's connection in terms of ∗gλν∗gλν", Nuovo cimento Soc. Ital. Fis. B, 27, pp.1297~1324 (1963)
  3. Datta, D.k., "Some theorems on symmetric recurrent tensors of the second order", Tensor (N.S.), 15, pp.1105~1136 (1964)
  4. Einstein, A., "The meaning of relativity" (1950), Princeton University Press
  5. Hlavaty, V., "Geometry of Einstein's unified field theory" (1957), Noordhoop Ltd
  6. Mishra, R.S., "n-dimensional considerations of unified field theory of relativity", Tensor, 9, pp.217~225 (1959)

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