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On the internal geometry of the normalized Penrosean. (Russian) Zbl 0708.53027
The Penrosean \(P(k)\) is the \(k\)-dimensional real manifold of null-planes of the hermiquadric (of signature null) in the complex projective space \(\mathbb CP^{2k}\). A normalization of the Penrosean is built, which generates connections of the first and the second kind. It is shown that all conformally-Euclidean spaces of the general theory of relativity may be included in the twistor program of Penrose.
MSC:
53B35 Local differential geometry of Hermitian and Kählerian structures
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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