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Slant submanifolds of a Lorentz Kenmotsu manifold. (English) Zbl 1425.53025

Summary: In this paper, we study slant submanifolds of a Lorentz Kenmotsu manifold. Necessary and sufficient conditions are given on a submanifold of a Lorentz Kenmotsu manifold to be a slant submanifold. We also study slant submanifolds of locally warped product Lorentz Kenmotsu manifold. We give examples of slant submanifold warped product a Lorentz Kenmotsu manifold. In addition, we investigate semi-slant submanifolds of a Lorentz Kenmotsu manifold. Moreover, we show that a semi-slant submanifold of locally warped product Lorentz Kenmotsu manifold is a warped product. Furthermore, we obtain some curvature properties for semi-slant submanifold of a Lorentz Kenmotsu space form. Finally, we show that if a semi-slant submanifold of a Lorentz Kenmotsu space form M is totally geodesic, then \(M\) is an \(\eta\)-Einstein manifold.

MSC:

53B25 Local submanifolds
53C40 Global submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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