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Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature
Chinese Annals of Mathematics, Series B, 2022 We study rotational hypersurfaces with constant Gauss-Kronecker curvature. We solve the ODE for the generating curves of such hypersurfaces and analyze several geometric properties of such hypersurfaces. In particular, we discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume ...
Liu, Yuhang, Dai, Yunchu
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Minimal Surfaces with Constant Gauss Curvature [PDF]
Proceedings of the American Mathematical Society, 1972 Minimal surfaces with constant Gauss curvature in real space forms are studied.
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Deformations Preserving Gauss Curvature [PDF]
, 2014 In industrial surface generation, it is important to consider surfaces with minimal areas for two main reasons: these surfaces require less material than non-minimal surfaces, and they are cheaper to manufacture. Based on a prototype, a so-called masterpiece, the final product is created using small deformations to adapt a surface to the desired shape.
Berres, Anne +2 more
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Swimming in Curved Surfaces and Gauss Curvature
Universitas Scientiarum, 2018 The Cartesian-Newtonian paradigm of mechanics establishes that, within an inertial frame, a body either remains at rest or moves uniformly on a line, unless a force acts externally upon it.
Leonardo Solanilla +2 more
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Surfaces Moving by Powers of Gauss Curvature [PDF]
Pure and Applied Mathematics Quarterly, 2012 We prove that strictly convex surfaces moving by $K^{ /2}$ become spherical as they contract to points, provided $ $ lies in the range $[1,2]$. In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution ...
Andrews, Ben, Chen, Xuzhong
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Hypersurfaces with planar lines of curvature in Euclidean Space
Selecciones Matemáticas, 2017 In this work, we present explicit parameterizations of hypersurfaces parameterized by lines of curvature with prescribed Gauss map and we characterize the hypersurfaces with planar curvature lines.
Carlos M. C. Riveros +1 more
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α-Gauss Curvature flows with flat sides
Journal of Differential Equations, 2013 In this paper, we study the deformation of the 2 dimensional convex surfaces in $\R^{3}$ whose speed at a point on the surface is proportional to $\alpha$-power of positive part of Gauss Curvature.
Kim, Lami, Lee, Ki-ahm, Rhee, Eunjai
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Holographic vector superconductor in Gauss–Bonnet gravity
Nuclear Physics B, 2016 In the probe limit, we numerically study the holographic p-wave superconductor phase transitions in the higher curvature theory. Concretely, we study the influences of Gauss–Bonnet parameter α on the Maxwell complex vector model (MCV) in the five ...
Jun-Wang Lu +5 more
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Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity
Journal of High Energy Physics, 2020 We investigate the neutral AdS black-hole solution in the consistent D → 4 Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett.
Xiongying Qiao +4 more
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Variational properties of the Gauss–Bonnet curvatures [PDF]
Calculus of Variations and Partial Differential Equations, 2007 The Gauss-Bonnet curvature of order $2k$ is a generalization to higher dimensions of the Gauss-Bonnet integrand in dimension $2k$, as the usual scalar curvature generalizes the two dimensional Gauss-Bonnet integrand. In this paper, we evaluate the first variation of the integrals of these curvatures seen as functionals on the space of all Riemannian ...
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