Complex Riemannian Geometry—Bianchi Identities and Einstein Tensor


Riemannian geometry has proved itself to be a useful model of the gravitational phenomena in the universe, but generalizations of it to include other forces have so far not been successful. Here we explore an extension of Riemannian geometry using a complex Hermitian metric tensor. We find that the standard electromagnetic field naturally appears along with two additional fields, which act as mass and charge sources. A first paper set up the basic geometry and derived the Christoffel symbols plus the E&M field equation. This paper continues development with the generalized Riemann curvature tensor, Bianchi identities and the Einstein tensor, laying the basis for field equations. A final paper will then present the field equations.

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Hutchin, R. (2015) Complex Riemannian Geometry—Bianchi Identities and Einstein Tensor. Journal of Modern Physics, 6, 1572-1585. doi: 10.4236/jmp.2015.611159.

Conflicts of Interest

The authors declare no conflicts of interest.


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