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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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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 Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space [PDF]
Journal of Function Spaces and Applications, 2013 By studying the Gauss map G and Laplace operator Δh of the second fundamental form h, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of ...
Minghao Jin, Donghe Pei, Shu Xu
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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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Pacific Journal of Mathematics, 1989 A construction is given whereby a Riemannian manifold induces a Riemannian metric on the total space of a large class of fibre bundles over it. Using this metric on the appropriate bundles, necessary and sufficient conditions are given for the Gauss map and the spherical Gauss map to be harmonic.
Jensen, Gary R., Rigoli, Marco
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Hypersurfaces with pointwise 1-type Gauss map in Lorentz–Minkowski space; 146–161 [PDF]
Proceedings of the Estonian Academy of Sciences, 2009 Hypersurfaces of a LorentzâMinkowski space Ln+1 with pointwise 1-type Gauss map are characterized. We prove that an oriented hypersurface Mq in Ln+1 has pointwise 1-type Gauss map of the first kind if and only if Mq has constant mean curvature and ...
Uğur Dursun
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Applied Sciences, 2023 High-dimensional systems are more secure than their lower-order counterparts. However, high security with these complex sets of equations and parameters reduces the transmission system’s processing speed, necessitating the development of an algorithm ...
Sharad Salunke +4 more
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SUBMANIFOLDS WITH BIHARMONIC GAUSS MAP [PDF]
International Journal of Mathematics, 2010 We generalize the Ruh–Vilms problem by characterizing the submanifolds in Euclidean spaces with proper biharmonic Gauss map and we construct examples of such hypersurfaces.
BALMUS A, MONTALDO, STEFANO, ONICIUC C.
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