New Classes and Stability Analysis of Deviation Tensors in Interdimensional Weak Null-Preserving Maps

We extend the theory of interdimensional weak null-preserving maps by provid- ing a complete local classification of the deviation tensor T based on its rank and kernel. We define weak k-plane null-preserving maps, examine their canonical de- composition, and analyze the local stability of T under small perturbations. Explicit examples illustrate the new classes of local behaviors. These results offer a rigor- ous and original contribution to the study of null structures in pseudo-Riemannian geometry.