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Creators/Authors contains: "Wilhelm, Frederick"

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  1. ; (, Annals of Global Analysis and Geometry)
    Agricola, Ilka; Bögelein, Verena (Ed.)
    Abstract Murphy and the second author showed that a generic closed Riemannian manifold has no totally geodesic submanifolds, provided the ambient space is at least four dimensional. Lytchak and Petrunin established a similar result in dimension 3. For the higher dimensional result, the “generic set” is open and dense in the$$C^{q}$$ C q –topology for any$$q\ge 2.$$ q ≥ 2 . In Lytchak and Petrunin’s work, the “generic set” is a dense$$G_{\delta }$$ G δ in the$$C^{q}$$ C q –topology for any$$q\ge 2.$$ q ≥ 2 . Here we show that the set of such metrics on a compact 3–manifold actually contains a set that is that is open and dense set in the$$C^{q}$$ C q –topology, provided$$q\ge 3.$$ q ≥ 3 .  
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    Free, publicly-accessible full text available May 15, 2026