Generalized warped products and the $\kappa$-nullity of Riemannian curvature

Abstract

In this short survey, we show how two (classes of) known examples of inhomogeneous, curvature homogeneous Riemannian manifolds with nontrivial $\kappa$-nullity can be seen as deformations of homogeneous metrics along the vertical distribution of an integrable Riemannian submersion. We also pose two open questions.

8 pages. arXiv admin note: text overlap with arXiv:2204.04551