Relevant bibliographies by topics / Umbilicity

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Umbilicity'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Umbilicity"

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Antić, Miroslava, Marilena Moruz, and Joeri Van der Veken. "H-Umbilical Lagrangian Submanifolds of the Nearly Kähler \( {\mathbb{S}^3\times\mathbb{S}^3} \)." Mathematics 8, no. 9 (2020): 1427. http://dx.doi.org/10.3390/math8091427.

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H-umbilicity was introduced as an analogue of total umbilicity for Lagrangian submanifolds since, in some relevant cases, totally umbilical Lagrangian submanifolds are automatically totally geodesic. In this paper, we show that, in the homogeneous nearly Kähler S3×S3, also H-umbilical Lagrangian submanifolds are automatically totally geodesic.
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Izumiya, Shyuichi, Donghe Pei, and María del Carmen Romero Fuster. "Umbilicity of space-like submanifolds of Minkowski space." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 2 (2004): 375–87. http://dx.doi.org/10.1017/s0308210500003267.

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We study some properties of space-like submanifolds in Minkowski n-space, whose points are all umbilic with respect to some normal field. As a consequence of these and some results contained in a paper by Asperti and Dajczer, we obtain that being ν-umbilic with respect to a parallel light-like normal field implies conformal flatness for submanifolds of dimension n − 2 ≥ 3. In the case of surfaces, we relate the umbilicity condition to that of total semi-umbilicity (degeneracy of the curvature ellipse at every point). Moreover, if the considered normal field is parallel, we show that it is ever
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DE LIMA, EUDES L., and HENRIQUE F. DE LIMA. "COMPLETE WEINGARTEN HYPERSURFACES SATISFYING AN OKUMURA TYPE INEQUALITY." Journal of the Australian Mathematical Society 109, no. 1 (2019): 81–92. http://dx.doi.org/10.1017/s1446788719000028.

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In this paper we deal with complete linear Weingarten hypersurfaces immersed into Riemannian space forms. Assuming an Okumura type inequality on the total umbilicity tensor of such hypersurfaces, we prove that either the hypersurface is totally umbilical or it holds an estimate for the norm of the total umbilicity tensor, which is also shown be sharp in the sense that the product of space forms realize them. Our approach is based on a version of the Omori–Yau maximum principle for a suitable Cheng–Yau type operator.
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Aquino, Cícero P., Márcio Batista, and Henrique F. de Lima. "On the umbilicity of generalized linear Weingarten hypersurfaces in hyperbolic spaces." Advances in Geometry 18, no. 4 (2018): 425–30. http://dx.doi.org/10.1515/advgeom-2018-0005.

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Abstract We deal with complete generalized linear Weingarten hypersurfaces immersed in hyperbolic spaces. Under appropriate constraints on the image of the Gauss map, we present suitable conditions which guarantee the umbilicity of these hypersurfaces.
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COLARES, ANTONIO GERVASIO, and FERNANDO ENRIQUE ECHAIZ-ESPINOZA. "CONSTANT SCALAR CURVATURE HYPERSURFACES WITH SECOND-ORDER UMBILICITY." Glasgow Mathematical Journal 51, no. 2 (2009): 219–41. http://dx.doi.org/10.1017/s0017089508004643.

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AbstractWe extend the concept of umbilicity to higher order umbilicity in Riemannian manifolds saying that an isometric immersion is k-umbilical when APk−1(A) is a multiple of the identity, where Pk(A) is the kth Newton polynomial in the second fundamental form A with P0(A) being the identity. Thus, for k=1, one-umbilical coincides with umbilical. We determine the principal curvatures of the two-umbilical isometric immersions in terms of the mean curvatures. We give a description of the two-umbilical isometric immersions in space forms which includes the product of spheres $S^{k}(\frac{1}{\sqr
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ROTH, JULIEN. "A NEW RESULT ABOUT ALMOST UMBILICAL HYPERSURFACES OF REAL SPACE FORMS." Bulletin of the Australian Mathematical Society 91, no. 1 (2014): 145–54. http://dx.doi.org/10.1017/s0004972714000732.

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AbstractIn this short note, we prove that an almost umbilical compact hypersurface of a real space form with almost Codazzi umbilicity tensor is embedded, diffeomorphic and quasi-isometric to a round sphere. Then, we derive a new characterisation of geodesic spheres in space forms.
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Cheng, Jih-Hsin, Hung-Lin Chiu, Jenn-Fang Hwang, and Paul Yang. "Umbilicity and characterization of Pansu spheres in the Heisenberg group." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 738 (2018): 203–35. http://dx.doi.org/10.1515/crelle-2015-0044.

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Abstract For every {n\geq 2} we define a notion of umbilicity for hypersurfaces in the Heisenberg group {H_{n}} . We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p-mean (or horizontal-mean) curvature in {H_{n}} up to Heisenberg translations.
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AQUINO, C. P., M. BATISTA, and H. F. DE LIMA. "ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE." Journal of the Australian Mathematical Society 103, no. 1 (2016): 45–58. http://dx.doi.org/10.1017/s1446788716000549.

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In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space$\mathbb{H}^{n+1}$, under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature. Furthermore, working with different warped product models for$\mathbb{H}^{n+1}$and supposing that certain natural inequalities involving two consecutive higher order mean curvature functions are satisfied, we study the rigidity and the nonexistence of complete hypersurfaces immersed in$\mathbb{H}^{n+1}$.
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Romero-Fuster, Marı́a del Carmen, and Federico Sánchez-Bringas. "Umbilicity of surfaces with orthogonal asymptotic lines in R4." Differential Geometry and its Applications 16, no. 3 (2002): 213–24. http://dx.doi.org/10.1016/s0926-2245(02)00068-2.

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Bezerra, A. C., and F. Manfio. "Umbilicity of constant mean curvature hypersurfaces into space forms." Journal of Mathematical Analysis and Applications 537, no. 2 (2024): 128316. http://dx.doi.org/10.1016/j.jmaa.2024.128316.

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Dissertations / Theses on the topic "Umbilicity"

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Perdigão, Tiago Rodrigo. "Semiumbilicidade e umbilicidade em superfícies imersas em Rn, n ≥ 4." Universidade Federal de Viçosa, 2011. http://locus.ufv.br/handle/123456789/4911.

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Made available in DSpace on 2015-03-26T13:45:33Z (GMT). No. of bitstreams: 1 texto completo.pdf: 445534 bytes, checksum: 6d9bec9dbcfd5842c82db998451fec95 (MD5) Previous issue date: 2011-02-23<br>In this work we introduce the concept of curvature ellipse at one point of a surface immersed in Rn, n &#8805; 4 to study the relationship between semiumbilics points (points that the curvature ellipse degenerated in a segment line), the existence of umbilic normal directions to the surface and hyperspherical surfaces. To achieve these goals we base our results especially in the articles &#8220;Umbil
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Pinheiro, Neilha Marcia. "Rigidez da esfera no espaÃo euclidiano." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11203.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Neste trabalho, provamos novos resutados de rigidez para hipersuperfÃcies quase-Einsteins no espaÃo euclidiano, baseado-se nos resultados pinching do autovalor. EntÃo, nÃs deduzimos alguns resultados anÃlogos para hipersuperfÃcies quase-umbÃlicas e uma nova caracterizaÃÃo de esferas geodÃsicas<br>In this work, we prove new rigidity results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable result for almost-umbilic hypersurfaces and new character
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Tshikunguila, Tshikuna-Matamba. "The differential geometry of the fibres of an almost contract metric submersion." Thesis, 2013. http://hdl.handle.net/10500/18622.

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Almost contact metric submersions constitute a class of Riemannian submersions whose total space is an almost contact metric manifold. Regarding the base space, two types are studied. Submersions of type I are those whose base space is an almost contact metric manifold while, when the base space is an almost Hermitian manifold, then the submersion is said to be of type II. After recalling the known notions and fundamental properties to be used in the sequel, relationships between the structure of the fibres with that of the total space are established. When the fibres are almost Hermiti
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Book chapters on the topic "Umbilicity"

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"Umbilici." In A Sense of Arrival. Duke University Press, 2024. http://dx.doi.org/10.1215/9781478059905-035.

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This penultimate part includes seven essays on the creation of, and reflection on, materialist art. Beginning with “Techne,” the practice of wire bending (only tangentially related to the Mas tradition) becomes a trope for considering the process of “unbinding” that was introduced in an earlier essay (“Conscientia”). This is followed by “Umbilici,” a series of art pieces with three corresponding poems and a reflection on the affective reach of witness. This is complicated by essays that emphasize transmediality as a rhetorical method for withholding and keeping secrets—of vernacular knowledge,
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"UMBILICI." In A Sense of Arrival. Duke University Press, 2024. http://dx.doi.org/10.2307/jj.20206645.37.

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"umbilicality, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/1020690887.

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"umbilicate, adj." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/4853792031.

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"umbilicate, v." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/4620623500.

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"umbilicary, adj." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/1675569906.

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"Key H: Umbilicate and Fan-Shaped Lichens." In Keys to Lichens of North America. Yale University Press, 2020. http://dx.doi.org/10.12987/9780300216257-011.

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"Key K: Foliose Lichens That Are Not Umbilicate, Jelly-Like, or Yellowish." In Keys to Lichens of North America. Yale University Press, 2020. http://dx.doi.org/10.12987/9780300216257-014.

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"„Conchae et umbilici" Eine motivgeschichtliche Betrachtung zu Cicero, De oratore 2,22f." In Psyche - Seele - anima. B. G. Teubner, 1998. http://dx.doi.org/10.1515/9783110934588-009.

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"Charles Street." In A Sense of Arrival. Duke University Press, 2024. http://dx.doi.org/10.1215/9781478059905-036.

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This penultimate part includes seven essays on the creation of, and reflection on, materialist art. Beginning with “Techne,” the practice of wire bending (only tangentially related to the Mas tradition) becomes a trope for considering the process of “unbinding” that was introduced in an earlier essay (“Conscientia”). This is followed by “Umbilici,” a series of art pieces with three corresponding poems and a reflection on the affective reach of witness. This is complicated by essays that emphasize transmediality as a rhetorical method for withholding and keeping secrets—of vernacular knowledge,
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Journal articles
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