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arXiv · 1109.6853

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

Jianquan Ge
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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.

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Jianquan Ge. 2013-03-12. DDVV-type inequality for skew-symmetric matrices and Simons-type inequality for Riemannian submersions. https://doi.org/10.1016/j.aim.2013.10.010

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