Abstract
We study characteristic r‐lightlike submanifolds M tangent to the characteristic vector fields in an indefinite metric 𝒮‐manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefinite 𝒮‐space form under suitable hypotheses: (1) M is totally umbilical or (2) its screen distribution S(TM) is totally umbilical in M.
Highlights
In the theory of submanifolds of semi-Riemannian manifolds, it is interesting to study the geometry of lightlike submanifolds due to the fact that the intersection of normal vector bundle and the tangent bundle is nontrivial, making it interesting and remarkably different from the study of nondegenerate submanifolds
Similar to Riemannian geometry, it is natural that indefinite S-manifolds are generalizations of indefinite Sasakian manifolds
They studied the geometry of lightlike hypersurfaces of indefinite S-manifold 6
Summary
In the theory of submanifolds of semi-Riemannian manifolds, it is interesting to study the geometry of lightlike submanifolds due to the fact that the intersection of normal vector bundle and the tangent bundle is nontrivial, making it interesting and remarkably different from the study of nondegenerate submanifolds. Many authors study lightlike submanifolds on indefinite Sasakian manifolds e.g., 1–4. Similar to Riemannian geometry, it is natural that indefinite S-manifolds are generalizations of indefinite Sasakian manifolds. Brunetti and Pastore analyzed some properties of indefinite S-manifolds and gave some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields 5. After they studied the geometry of lightlike hypersurfaces of indefinite S-manifold 6. The objective of this paper is to study characteristic r-lightlike submanifolds M of an indefinite S-manifold M subject to the conditions: 1 M is totally umbilcial, or 2 S T M. Afterwards, we study characteristic r-lightlike submanifolds of M in Sections 4 and 5
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