DDVV-type inequality for skew-symmetric matrices and Simons-type inequality for Riemannian submersions

Abstract

In this paper, we will first derive a DDVV-type optimal inequality for real skew-symmetric matrices, then we apply it to establish a Simons-type integral inequality for Riemannian submersions with totally geodesic fibres and Yang-Mills horizontal distributions. In this way, we show phenomenons of duality between Submanifold geometry and Riemannnian submersion, particularly between second fundamental form of a submanifold and integrability tensor of a Riemannian submersion.

27 pages

References in corpus (2)

• Remarks on an inequality involving the normal scalar curvature
• A survey on the DDVV conjecture

Cited by in corpus (6)

• On some conjectures by Lu and Wenzel
• Curvatures of Stiefel manifolds with deformation metrics
• Shrinkage Estimation of the Frechet Mean in Lie groups
• Differentiable classification of 4-manifolds with singular Riemannian foliations
• Some generalizations of the DDVV and BW inequalities
• DDVV-type inequality for Hermitian matrices