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Zbl 0608.53053
Duggal, K.L.
CR-structures and Lorentzian geometry. (English)
[J] Acta Appl. Math. 7, 211-223 (1986). ISSN 0167-8019; ISSN 1572-9036/e

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.
[A.Bejancu]

MSC 2000:: *53C40 Submanifolds (differential geometry)
53C50 Lorentz manifolds, manifolds with indefinite metrics

Keywords: CR-submanifold; totally umbilical; Lorentz manifold; affine conformal motion

Citations: Zbl 0605.53001

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