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Results tagged with riemannian-geometry
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user 9833
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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What is a random eigenfunction on the hyperbolic plane?
Is there an (invariant under isometries) notion of a random eigenfunction on the hyperbolic plane, for a given eigenvalue?
It is a reference request because the answer is probably positive and I even …
- 6,891
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Complex surfaces not admitting nonnegative sectional curvature metrics
Five simply connected closed 4-manifolds are known to admit Riemannian metrics with nonnegative sectional curvature:
$$\mathbb{S}^4,\,\mathbb{C}\mathbb{P}^2,\,\mathbb{S}^2\times\mathbb{S}^2,\,\mathbb …
- 3,751
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Can we specify the value of harmonic forms at a point?
Take a torus $\mathbb{T}^d$ of dimension $d$ and introduce on it such a metric that some part of it would be isometric to a (sufficiently small) neighbourhood $U$ of $p\in M$. By Hodge theory, harmon …
- 6,891