The curvature tensors in the Einstein's $^{\ast}g$-unified field theory II. The contracted SE-curvature tensors of $^{\ast}g$-SEX$_n$
Bull. Korean Math. Soc. 1998 Vol. 35, No. 4, 641-650
Kyung Tae Chung, Phil Ung Chung, and In Ho Hwang
Yonsei University, Kangwon National University, University of Inchon
Abstract : Chung and et al. ([2], 1991) introduced a new concept of a manifold, denoted by $^*g$-SEX$_n$, in Einstein's $n$-dimensional ${}^*g$-unified field theory. The manifold $^*g$-SEX$_n$ 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 SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor $^*g^{\lambda \nu}$. Recently, Chung and et al. ([3], 1998) obtained a concise tensorial representation of SE-curvature tensor defined by the SE-connection of $^*g$-SEX$_n$ and proved several identities involving it. \indent This paper is a direct continuation of [3]. In this paper we derive surveyable tensorial representations of contracted curvature tensors of $^*g$-SEX$_n$ and prove several generalized identities involving them. In particular, the first variation of the generalized Bianchi's identity in $^*g$-SEX$_n$, proved in Theorem (2.10a), has a great deal of useful physical applications.
Keywords : manifold $^*g$-SEX$_n$, contracted SE-curvature tensors
MSC numbers : 83E50, 83C05, 58A05
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