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- W4287635880 abstract "We study the geometry of surfaces in $mathbb R^5$ by relating it to the geometry of regular and singular surfaces in $mathbb R^4$ obtained by orthogonal projections. In particular, we obtain relations between asymptotic directions, which are not second order geometry for surfaces in $mathbb R^5$ but are in $mathbb R^4$. We also relate the umbilic curvatures of each type of surface and their contact with spheres. We then consider the surfaces as normal sections of 3-manifolds in $mathbb R^6$ and again relate asymptotic directions and contact with spheres by defining an appropriate umbilic curvature for 3-manifolds." @default.
- W4287635880 created "2022-07-25" @default.
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- W4287635880 date "2020-10-21" @default.
- W4287635880 modified "2023-09-27" @default.
- W4287635880 title "Geometry of surfaces in $mathbb R^5$ through projections and normal sections" @default.
- W4287635880 doi "https://doi.org/10.48550/arxiv.2010.10976" @default.
- W4287635880 hasPublicationYear "2020" @default.
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