Pointwise slant lightlike submersions

Purpose The study aims to develop and investigate a new geometric notion called pointwise slant lightlike submersions defined from an indefinite Kaehler manifold to a lightlike manifold. It seeks to extend earlier concepts in the field, provide characterizations that describe when such submersions exist, identify conditions under which they reduce to ordinary slant lightlike submersions and analyze various geometric properties associated with them. Design/methodology/approach We develop the framework of pointwise slant lightlike submersions by combining techniques from lightlike geometry and the theory of submersions on indefinite Kaehler manifolds. Using the structure tensors of the ambient manifold, we derive characterization conditions for the existence of such submersions. Differential geometric tools – such as decompositions of tangent bundles, properties of the radical distribution and behavior of the Kaehler structure – are employed to analyze when a pointwise slant lightlike submersion reduces to a slant lightlike submersion. Various curvature and integrability conditions are examined to study their geometric properties. Findings The study establishes necessary and sufficient conditions for the existence of pointwise slant lightlike submersions and identifies the geometric constraints that determine when such a submersion becomes a slant lightlike submersion. Several structural results concerning the behavior of the slant function, integrability of distributions and curvature properties are obtained. The research reveals how the interaction between the complex structure and lightlike geometry influences the submersion's behavior, offering new insights into the geometry of indefinite Kaehler manifolds. Originality/value This work introduces the notion of pointwise slant lightlike submersions, a concept not previously studied in the literature. It unifies and extends existing theories of pointwise slant submersions and slant lightlike submersions into a broader geometric framework. The characterization theorems and geometric conditions derived here provide new tools for studying lightlike geometry and submersion theory on indefinite Kaehler manifolds. The results contribute original insights and establish a foundation for further research in differential geometry, particularly in the study of lightlike phenomena and Kaehler structures.