Byrnes, G. B. Non-definite complex manifolds: an alternative gauge theory? (English) Zbl 0641.53080 Classical Quantum Gravity 4, 1347-1356 (1987). The structure of a complex manifold with a complex bilinear pseudo-metric structures is investigated. A topological consequence of the existence of such metric is the possibility of foliating a complex 4-dimensional manifold \(V_ 4\) into real 4-dimensional submanifolds. The author studies the behaviour of geodesics on \(V_ 4\) and thus implicitly the motion of test particles. Particles which follow complex geodesics of the manifold have quantum-like behaviour. Reviewer: St.Ianus MSC: 53C80 Applications of global differential geometry to the sciences 83E15 Kaluza-Klein and other higher-dimensional theories Keywords:complex manifold; pseudo-metric structures; motion of test particles; geodesics PDFBibTeX XMLCite \textit{G. B. Byrnes}, Classical Quantum Gravity 4, 1347--1356 (1987; Zbl 0641.53080) Full Text: DOI