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arXiv · 1706.09211

An intrinsic curvature condition for submersions over Riemannian manifolds

Llohann D. Sperança
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Abstract

Let $\pi{:}\,(M,\mathcal{H})\to (B,b)$ be a submersion equipped with a horizontal connection $\cal H$ over a Riemannian manifold $(B,b)$. We present an intrinsic curvature condition that only depends on the pair $(\cal H,b)$. By studying a set of relative flat planes, we prove that a certain class of pairs $(\cal H,b)$ admits a compatible metric with positive sectional curvature only if they are \textit{fat}, verifying Wilhelm's Conjecture in this class.

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Llohann D. Sperança. 2017-06-28. An intrinsic curvature condition for submersions over Riemannian manifolds. https://arxiv.org/abs/1706.09211

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