The integral constraint vectors of Traschen and three-surface twistors. (English) Zbl 0661.53018
An integral constraint vector or ICV on a spacelike hypersurface \(\Sigma\) in a space-time is a vector field tangent to \(\Sigma\) satisfying two differential equations involving the first and the second fundamental forms of \(\Sigma\). The author interprets an ICV as a covariant constant object with respect to a connection depending on \(\Sigma\). So, the existence of ten linearly independent ICVs is reduced to the finding of the conditions for the vanishing of the curvature of this connection. These conditions are interpreted in terms of embeddability of \(\Sigma\) in a space of constant curvature. Finally, the ICVs are related to three- surface twistors.
Reviewer: M.Anastasiei
MSC:
53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
53C80 | Applications of global differential geometry to the sciences |
Keywords:
integral constraint vector; spacelike hypersurface; fundamental forms; connection; three-surface twistorsReferences:
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