An optimal matrix inequality and its applications to geometry of Riemannian submersions

Details An optimal matrix inequality and its applications to geometry of Riemannian submersions An optimal matrix inequality and its applications to geometry of Riemannian submersions

2011-09-30

arxiv.org/abs/1109.6853v1

Mathematics

Differential Geometry

25 pages

Scientific paper

Motivated by the matrix form of the DDVV conjecture in submanifold geometry which is an optimal inequality involving norms of commutators of several real symmetric matrices and takes an important role in the proof of the well-known Simons inequality for closed minimal submanifolds in spheres, in this paper we first derive a similar optimal inequality of real skew-symmetric matrices, then we apply it to establish a Simons-type inequality for Riemannian submersions, which shows another "evidence" of the duality between submanifold geometry and Riemannian submersions.

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