DDVV conjecture for Riemannian maps from quaternionic space forms
Kirti Gupta, Punam Gupta
TL;DR
The paper extends the DDVV-type inequality to Riemannian maps from quaternionic space forms, deriving explicit bounds that relate intrinsic curvature of the domain, extrinsic curvature of the map, and quaternionic ambient curvature. The main results include a 4–Ricci-type inequality for the horizontal distribution and a normalized scalar-curvature bound, along with clear equality characterizations tied to the vanishing of the map’s second fundamental form in certain directions. This work integrates quaternionic Kähler geometry, Riemannian map theory, and submanifold-style curvature inequalities, offering potential rigidity results and applications in quaternionic geometry and related physical theories.
Abstract
In this paper, we investigate the DDVV-type inequality for Riemannian maps from quaternionic space forms to Riemannian manifolds. We also discuss the equality case of the derived inequality with application.