Marcus's Theorem

A compact manifold admits a Lorentzian structure iff its Euler characteristic vanishes. Therefore, every noncompact manifold admits a Lorentzian structure.

See also

Euler Characteristic, Lorentzian Structure

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Dodson, C. T. J. and Parker, P. E. "Marcus's Theorem." §9.5 in A User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, pp. 289-291, 1997.

Referenced on Wolfram|Alpha

Marcus's Theorem

Cite this as:

Weisstein, Eric W. "Marcus's Theorem." From MathWorld--A Wolfram Web Resource.

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