Coisotropic warped product submanifolds of a mixed 3-Sasakian statistical manifold. (English) Zbl 07880124
Summary: In this paper, we study the geometry of invariant lightlike submanifolds of a mixed 3-Sasakian statistical manifold. We characterize the integrability of the various distributions of them with respect to their totally geodesic nature and the statistical shape operators. We also characterize totally umbilical distributions of a warped product lightlike submanifolds of a statistical manifold. Moreover, we show that invariant lightlike submanifolds of a mixed 3-Sasakian statistical manifold with tangent structure vector fields inherit a mixed 3-Sasakian statistical structure. Further, we give an example of a specific type of coisotropic warped product submanifold of a mixed 3-Sasakian statistical manifold which is not an invariant submanifold.
MSC:
| 53Cxx | Global differential geometry |
| 53Bxx | Local differential geometry |
| 62Fxx | Parametric inference |
Keywords:
lightlike submanifold; mixed 3-structure manifold; statistical structure; warped product lightlike submanifoldReferences:
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