Characterizations of slant-type submanifolds in $(\alpha ,p)$-golden geometry

Motivated by the growing interest in geometric structures defined through polynomial tensor identities, we investigated slant and semi-slant submanifolds of almost $(\alpha ,p)$-golden Riemannian manifolds a generalized class encompassing golden, and complex golden structures. We introduced the notions of $(\alpha ,p)$-slant and semi-slant submanifolds, established their characterizations and integrability conditions, and constructed illustrative examples. The results extend and unify existing theories in golden and complex golden geometry within a common framework.