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On contact CR-lightlike submanifolds of indefinite Sasakian manifolds. (English) Zbl 1220.53028
Summary: We obtain a condition for an invariant light-like submanifold of an indefinite Sasakian space form to be of constant \(\phi\)-sectional curvature. Then, we study contact CR-light-like submanifolds of \((\varepsilon)\)-Sasakian manifolds extensively and conclude with a study of totally contact umbilical contact CR-light-like submanifolds.

MSC:
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D15 Almost contact and almost symplectic manifolds
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