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umbilic
▪ I. umbilic, n. (ʌmˈbɪlɪk) Forms: α. 7 vmbilike, -icke, umbilick, umbelic(k, 7, 9 umbilic. β. 7 vmbilique, umbelique. [ad. L. umbilīc-us umbilicus, related to Gr. ὀµϕαλός, and ultimately to navel n. Hence also F. ombilic, † umbilic (1556), It. um-, ombilico, ombellico, Sp. ombligo, Pg. umbigo. In s... Oxford English Dictionary
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Umbilic torus
The umbilic torus or umbilic bracelet is a single-edged 3-dimensional shape. Christopher Zeeman named this set the umbilic bracelet in 1976. The torus is defined by the following set of parametric equations. wikipedia.org
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umbelick
umbelic(k, -ique obs. forms of umbilic n. Oxford English Dictionary
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Umbilical point
The sphere is the only surface with non-zero curvature where every point is umbilic. A flat umbilic is an umbilic with zero Gaussian curvature. A submanifold is said to be umbilic (or all-umbilic) if this condition holds at every point "p". wikipedia.org
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umbilicar
umˈbilicar, a. Geom. [f. umbilic-us + -ar. Cf. late L. umbilīcāris (Tertullian).] Of or belonging to the umbilicus.1843 MacCullagh in Proc. R. Irish Acad. (1846) II. 458 A focal which is not modular may be called umbilicar, because it intersects the surface in the umbilics. Ibid. 469 A focal point w... Oxford English Dictionary
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Ridge (differential geometry)
There are two main cases: one has three ridge lines passing through the umbilic, and the other has one line passing through it. wikipedia.org
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Every point in S is umbilical $\rightarrow $ S is a plane or sphere. Umbilic points on a connected smooth surface problem Here we have a proof that if every point in a surface $S\subset\mathbb{R}^3$ is umbilical then...
A topological space $X$ is called locally path connected if every $x \in X$ is contained in a neighborhood $U$ which is path connected. If $X$ is locally path connected, then it is connected iff it is path connected. We know that path connected implies connected always. To see the reverse implicatio...
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Cubic form
The equivalence classes of such cubics form a three-dimensional real projective space and the subset of parabolic forms define a surface – the umbilic wikipedia.org
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What are the umbilic hypersurfaces in a sphere? It is a well-known result that all umbilic hypersurfaces (complete and connected, say) of $\mathbb{R}^n$ are spheres or planes. But what can we say about umbilic hypersu...
Spivak's comprehensive introduction to Differential Geometry, Vol 4 2n edition, page 112.
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Helaman Ferguson
His most widely known piece of art is a 69 cm (27") bronze sculpture, Umbilic Torus. See also Umbilic torus References External links Home page Celebrating Mathematics in Stone and Bronze by Helaman and Claire Ferguson, Notices of wikipedia.org
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parumbilical
parumbilical, a. Anat. (pærʌmˈbɪlɪkəl) [f. para-1 + L. umbilic-us navel + -al1.] Situated around or close to the umbilicus or navel.1890 in Century Dict. 1893 Syd. Soc. Lex., Parumbilical veins. 1897 Allbutt's Syst. Med. IV. 178 The passage of blood from the portal vein, by the parumbilical vein to ... Oxford English Dictionary
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The Swallow's Tail
possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": fold, cusp, swallowtail, butterfly, hyperbolic umbilic , elliptic umbilic, and parabolic umbilic. wikipedia.org
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Focal surface
When the surface has a ridge the focal surface has a cuspidal edge, three such edges pass through an elliptical umbilic and only one through a hyperbolic umbilic. wikipedia.org
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Local eigenvectors frame of a isometric immersion I have a little (possible dumb) technical question about local eigenvectors frame of a isometric immersion. Let $N^n$ a smooth manifold and $(M^{n+1},g)$ a smooth Rie...
However, in dimension $n>2$, it's not good enough to say there are no umbilic points; you actually need to require distinct eigenvalues.
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Torus (disambiguation)
Torus knot Algebraic torus Umbilic torus Genus-2 surface, also called "double torus" Maximal torus Clifford torus Medicine Torus palatinus, a wikipedia.org
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