APM  Vol.4 No.11 , November 2014
Complex Spacetime Frame: Four-Vector Identities and Tensors
Author(s) Joseph Akeyo Omolo*
ABSTRACT
This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.

Cite this paper
Omolo, J. (2014) Complex Spacetime Frame: Four-Vector Identities and Tensors. Advances in Pure Mathematics, 4, 567-579. doi: 10.4236/apm.2014.411065.
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