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Results tagged with riemannian-geometry
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user 409915
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.
7
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Is the bundle map of the Eguchi-Hanson metric a Riemannian submersion?
Background. (Can be skipped if you already know what is the Eguchi-Hanson metric.) The Eguchi-Hanson metric $g$ is a complete Ricci-flat Riemannian metric on the cotangent bundle of the 2-sphere, $T^* …
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3
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answer
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Dirichlet-type condition on Riemannian manifold
Let $M$ be a Riemannian manifold and $S \subset M$ a compact submanifold of strictly lower dimension. Does every smooth function on $S$ extend to a harmonic function on a neighborhood of $S$?
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4
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Ricci curvature of totally geodesic submanifold
Let $M$ be a Ricci-flat Riemannian manifold and $N \subset M$ a totally geodesic submanifold. Is $N$ also Ricci-flat?
A partial result in that direction is that the Ricci curvature of $N$ is given by
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