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Abstract
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In this paper, we study the geometry of invariant lightlike submanifolds of amixed 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.
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