Rotation hypersurfaces in spaces of constant curvature

Carmo, Manfredo do; Dajczer, Marcos

doi:10.1090/s0002-9947-1983-0694383-x

Cited by 180 publications

(128 citation statements)

References 7 publications

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“…Let (x, y, z) denote the Cartesian coordinates of the Euclidean space. It follows from the classical work of Charles Delaunay [1] the existence of an immersed, non embedded, curve N r in the half plane…”

Section: Preliminary Resultsmentioning

confidence: 99%

A Note on Doubly Connected Surfaces of Constant Mean Curvature with Prescribed Boundary

2006

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Given two convex curves γ 1 , γ 2 in parallel planes π 1 , π 2 of R 3 respectively, being γ 2 the orthogonal projection of γ 1 on π 2 . We prove in [1] the existence of a cmc surface spanning γ 1 , γ 2 , under hypotheses relating the geometry of the curves, the distance between the planes and the mean curvature. We also proved that the surface is a radial graph over a unit sphere. References[1] Aiolfi, A. J., Fusieger, P. and Ripoll, J. A note on doubly connected surfaces of constant mean curvature with prescribed boundary

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Section: Preliminary Resultsmentioning

confidence: 99%

A Note on Doubly Connected Surfaces of Constant Mean Curvature with Prescribed Boundary

2006

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“…We may quote the classic work [2], studying rotational (i.e., O(2)-invariant) constant mean curvature surfaces, or the analysis and classification of O(n)-invariant minimal hypersurfaces in space forms carried out in [3].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

O(m) � O(n)-Invariant Minimal Hypersurfaces in $\mathbb{R}$ m+n

et al. 2005

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A b s tra c t Complex common names such as Indian elephant or green tea denote a certain type o f entity, viz. kinds. Moreover, those kinds are always subkinds o f the kind denoted by their head noun. Establishing such subkinds is essentially the task o f classifying modifiers that are a defining trait of endocentrically structured complex common names. Examining complex common names of different lexico-syntactic types (N N compounds, N + N syntagmas, N P /P P syntagmas, A + N syntagmas) and from different languages (particularly English, G erm an and French) it can be shown that complex common names are subject to language-independent formal and semantic constraints. In particular, complex common names qualify as name-like expressions in that they tend to be deficient in term s of formal complexity and semantic compositionality.

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“…In this paper, we show that 2 3 is a complex 3-manifold, equipped with a Mobius invariant Hermitian metric h of type (1,2). So the geodesics with respect to the Lorentz metric = Re(ℎ) on form a one-parameter family of time-like pseudo circles in 1 3 , which is so-called generalized helicoid in a space form with zero mean curvature.…”

Section: Introductionmentioning

confidence: 85%

Automatic Control System Based on the Internet of Street Lamp Illumination

Fan¹

2016

Advanced Science and Technology Letters

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Abstract.With the continuous development of information technology, the application level of city information is increasing. A model based on Internet of street lamp illumination by automatic control system is designed in this paper. Based on intensity of illumination, and traffic noise, the information such as temperature and humidity automatic data collection and information processing, the system sets the corresponding weights of each measurement parameter, through the corresponding algorithm to judge the different road and weather conditions and make the corresponding instruction, implement different road and weather conditions of intelligent street lamp illumination adjustment function.We designed a partial state observer to estimate it easily utilizing the vibrations of car-body and bogie frame. And the vertical vehicle dynamic system model was built and simulated with the track irregularity as excitation to product the corresponding vibrations, and thus, to validate the feasibility of the observer, as well as the observer performances of estimation errors and convergence time. In this paper, we study the moduli space 2 3 of time-like pseudo circles in 1 3 . Up to Möbius transformations, all the geodesics in 2 3 are determined to form a one-parameter family of time-like pseudo circles on a generalized helicoid in space form 1 3 (1), 1 3 (−1), 1 3 (0)，resp.

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Rotation hypersurfaces in spaces of constant curvature

Cited by 180 publications

References 7 publications

A Note on Doubly Connected Surfaces of Constant Mean Curvature with Prescribed Boundary

A Note on Doubly Connected Surfaces of Constant Mean Curvature with Prescribed Boundary

O(m) � O(n)-Invariant Minimal Hypersurfaces in $\mathbb{R}$ m+n

Automatic Control System Based on the Internet of Street Lamp Illumination

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