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Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. (English) Zbl 1296.53041
Summary: In this paper we prove some properties of indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define $$D$$-totally geodesic and $$D^\bot$$-totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.
##### MSC:
 53B25 Local submanifolds 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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