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Results tagged with riemannian-geometry
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user 530303
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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Upper bound on the sectional curvature of a Riemannian submersion
Consider the manifold $M := \operatorname{SO}(n) \times \mathbb{S}^{n-1}$, endowed with the product metric given by the bi-invariant metric of $\operatorname{SO}(n)$ and the round metric of $\mathbb{S …
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Riemannian submersions and associated fibre bundles
My question is as follows, it is related to the chapter of Associated Fibre Bundles from [1].
Let $(X, g_X)$ and $(Y, g_Y)$ be two smooth manifolds and let $H$ be a Lie group which acts smoothly on bo …
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