Geometry of the submanifolds of \(SEX_ n\). I: The C-nonholonomic frame of reference
type: Item
instance of: scholarly article
title: Geometry of the submanifolds of \(SEX_ n\). I: The C-nonholonomic frame of reference
zbMATH Open document ID: 0698.53008
DOI: 10.1007/BF00669999
author: Kyung Tae Chung
author: Keum Sook So
author: Jongwoo Lee
published in: International Journal of Theoretical Physics
publication date: 1989-01-01T00:00:00Z
review text: [For part II, see the review below Zbl 0698.53009.] In 1950 Einstein proposed [see \textit{A. Einstein}, The meaning of relativity (Princeton 1950; Zbl 0037.420)] a new unified field theory that would include both gravitation and electromagnetism. Although the intent of this theory is physical, its exposition is mainly geometrical. It may be characterized as a set of geometrical postulates for the space- time \(X_ 4\). However, the geometrical consequences of these postulates were not developed very far by Einstein. Characterizing Einstein's 4- dimensional unified field theory as a set of geometrical postulates for \(X_ 4\), \textit{V. Hlavatý} [Geometry of Eintein's unified field theory (Noordhoop 1957; Zbl 0078.433)] gave its mathematical foundation for the first time. Since then the geometrical consequences of these postulates have been developed very far, mainly by Hlavatý. A number of mathematicians and theoretical physicists have contributed to the development of this theory. Generalizing \(X_ 4\) to an n-dimensional generalized Riemannian manifold \(X_ n\), \textit{R. C. Wrede} [Tensor, New. Ser. 8, 95-122 (1958; Zbl 0080.219)] studied Principles A and B of Einstein's unified field theory for the first time. But this solution of Einstein's equations is not surveyable. Hlavatý's solution for the first class in \(X_ 4\) is not surveyable either. Later, \textit{K. T. Chung} [Nuovo Cimento, X. Ser. 27, 1297-1324 (1963; Zbl 0115.436)] gave a very handy and clear solution in the 4-dimensional g-unified field theory using the method of substitution. Recently, \textit{K. T. Chung} and \textit{C. H. Cho} [Nuovo Cimento 100 B, 537-550 (1987)] introduced the concept of the n-dimensional SE manifold \(SEX_ n\), imposing a semisymmetric condition on \(X_ n\), and found a unique representation of Einstein's connection in a beautiful and clear form. Later, \textit{K. T. Chung} and \textit{I. Y. Lee} [Int. J. Theor. Phys. 27, No.9, 1083-1104 (1988; Zbl 0652.53057); and \text…
Mathematics Subject Classification ID: 53B15
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83E15
zbMATH DE Number: 4144855
zbMATH Keywords: unified field theory
zbMATH Keywords: SE manifold
zbMATH Keywords: semisymmetric condition
zbMATH Keywords: Einstein's connection
zbMATH Keywords: C-nonholonomic frame of reference
reviewed by: Radu Iordănescu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00669999
OpenAlex ID: W2080150912
description: scientific article; zbMATH DE number 4144855