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AIMS Mathematics, 2023 In this study, the ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are introduced in Euclidean 3-space.
Yanlin Li +3 more
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The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature [PDF]
Anais da Academia Brasileira de Ciências, 2013 In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature. We give a different proof of the following theorem of R.
PEDRO A. HINOJOSA, GILVANEIDE N. SILVA
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Classification of Complete Degenerate Stationary Surfaces in
Mathematics, 2022 In this paper, we classify the complete degenerate stationary surfaces in R3,1 with injective Gauss maps.
Li Ou, Ling Yang
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The Gauss map and secants of the Kummer variety [PDF]
Bulletin of the London Mathematical Society, 2019 Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian, and prove that the Gauss map of ...
Auffarth, Robert +2 more
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5D Gauss Map Perspective to Image Encryption with Transfer Learning Validation
Applied Sciences, 2022 Encryption of visual data is a requirement of the modern day. This is obvious and greatly required due to widespread use of digital communication mediums, their wide range of applications, and phishing activities.
Sharad Salunke +4 more
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Surfaces with $1$-type Gauss map [PDF]
Kodai Mathematical Journal, 1996 The author proves the following theorem. Let \(M\) be an orientable connected surface of Euclidean 3-space \(E^3\). Then \(M\) has 1-type Gauss map if and only if \(M\) is an open part of a sphere or an open part of a circular cylinder. Reviewer's remark: Compact submanifolds of Euclidean spaces with 1-type Gauss map were completely classified in ...
Chang-Rim Jang
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On the Gauss map of equivariant immersions in hyperbolic space [PDF]
Journal of Topology, 2020 Given an oriented immersed hypersurface in hyperbolic space Hn+1$\mathbb {H}^{n+1}$ , its Gauss map is defined with values in the space of oriented geodesics of Hn+1$\mathbb {H}^{n+1}$ , which is endowed with a natural para‐Kähler structure.
Christian El Emam, Andrea Seppi
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The geometry of Gauss map and shape operator in simply isotropic and pseudo-isotropic spaces [PDF]
Journal of Geometry, 2019 In this work, we are interested in the differential geometry of surfaces in simply isotropic $${\mathbb {I}}^3$$I3 and pseudo-isotropic $${\mathbb {I}}_{\mathrm {p}}^3$$Ip3 spaces, which consists of the study of $${\mathbb {R}}^3$$R3 equipped with a ...
Luiz C. B. da Silva
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Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map [PDF]
, 2015 In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere $\mathbb{S}^4_s(1)$ with index s, $s=1, 2$, and having ...
Bektaş, Burcu +2 more
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Exploring Simplicity Bias in 1D Dynamical Systems [PDF]
EntropyArguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input–output maps. This phenomenon is known as simplicity bias.
Kamal Dingle +3 more
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