Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON THE ALGEBRA OF 3-DIMENSIONAL ES-MANIFOLD

  • Hwang, In Ho (Department of Mathematics Incheon National University)
  • Received : 2014.01.18
  • Accepted : 2014.03.25
  • Published : 2014.03.30
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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.

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References

  1. Hwang, I.H., A study on the geometry of 2-dimensional RE-manifold $X_2$, J. Korean Math. Soc. 32 (2) (1995), 301-309.
  2. Chung, K.T., Einstein's connection in terms of $^*g^{{\lambda}{\nu}}$, Nuovo cimento Soc. Ital. Fis. B 27 (1963), 1297-1324.
  3. Datta, D.k., Some theorems on symmetric recurrent tensors of the second order, Tensor (N.S.) 15 (1964), 1105-1136.
  4. Einstein, A., The meaning of relativity, Princeton University Press, 1950.
  5. Hlavaty, V., Geometry of Einstein's unified field theory, Noordhoop Ltd., 1957.
  6. Mishra, R.S., n-dimensional considerations of unified field theory of relativity, Tensor 9 (1959), 217-225.

Cited by

  1. EINSTEIN'S CONNECTION IN 3-DIMENSIONAL ES-MANIFOLD vol.23, pp.2, 2015, https://doi.org/10.11568/kjm.2015.23.2.313