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CR-structures and Lorentzian geometry. (English) Zbl 0608.53053
The paper is dealing with interrelations between Cauchy-Riemann structures and Lorentzian geometry. First, the author studies the concept of CR-submanifold [see the reviewer, Geometry of CR-submanifolds (Dordrecht, 1986; Zbl 0605.53001)] in a Lorentz manifold. He proves that a totally umbilical CR-submanifold of a Lorentz manifold is not necessarily totally geodesic provided the holomorphic distribution is light-like. Then he introduces and studies the concept of affine conformal motion and obtains characterizations of Lorentzian manifolds admitting an infinitesimal affine conformal motion.
Reviewer: A.Bejancu
MSC:
53C40Global submanifolds (differential geometry)
53C50Lorentz manifolds, manifolds with indefinite metrics
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