Null geodesic surfaces and Goldberg–Sachs theorem in complex Riemannian spaces

Journal Article · Wed Jan 01 04:00:00 EST 1975 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.522506· OSTI ID:4130943

Plebañski, J. F.

An extension of the Goldberg--Sachs theorem for the case of a complex V$sub 4$ is given with a simple proof. The interpretation of the theorem, however, no longer applies the concept of the geodesic and shearless congruence of null directions; instead, the existence of a geodesic 2-surface (complex), the tangent vectorial space to which (I) contains only null vectors, (II) is parallelly propagated along the surface, is now essential. (AIP)

• Research Organization: Centro de Investigacion y de Estudios Avanzados del IPN, Mexico 14, D.F., Mexico
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-011180
• OSTI ID: 4130943
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 16; ISSN JMAPAQ; ISSN 0022-2488
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

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