Results 1 to 10 of about 483 (49)
Helicoidal Surfaces in Galilean Space With Density
Frontiers in Physics, 2020 In this paper, we construct helicoidal surfaces in the three dimensional Galilean space G3. The First and the Second Fundamental Forms for such surfaces will be obtained. Also, mean and Gaussian curvature given by smooth functions will be derived.
Safaa Mosa +3 more
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Differential geometry of grassmannians and the Plücker map [PDF]
Open Mathematics, 2012 Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were ...
Anan’in Sasha, Grossi Carlos
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Examples of noncompact nonpositively curved manifolds
Bulletin of the London Mathematical Society, Volume 53, Issue 4, Page 1061-1071, August 2021., 2021 Abstract We give a simple construction of new, complete, finite volume manifolds M of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are not duality groups.
Grigori Avramidi +1 more
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Mannheim curves and their partner curves in Minkowski 3-space E13
Demonstratio Mathematica, 2022 The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski ...
Elsharkawy Ayman, Elshenhab Ahmed M.
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On the dual quaternion geometry of screw motions
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this study, the screw motions are studied using dual quaternions with the help of di erent perspectives. Firstly, orthogonality definition of dual quaternions is given and geometric interpretation of orthogonality condition is made.
Erişir Tülay +3 more
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Elastic Sturmian spirals in the Lorentz-Minkowski plane
Open Mathematics, 2016 In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form.
Uçum Ali +2 more
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Curves in the Lorentz-Minkowski plane with curvature depending on their position
Open Mathematics, 2020 Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in the Lorentz-Minkowski plane, focusing on spacelike
Castro Ildefonso +2 more
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, 2014 We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries.
A. Papadopoulos, N. A'campo
semanticscholar +1 more source
Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers
Open Mathematics, 2018 This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2 whose curvature is expressed in terms of the Lorentzian ...
Castro Ildefonso +2 more
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On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three‐space
Abstract and Applied Analysis, Volume 7, Issue 3, Page 113-123, 2002., 2002 This paper proves that any nonregular nonparametric saddle surface in a three‐dimensional space of nonzero constant curvature k, which is bounded by a rectifiable curve, is a space of curvature not greater than k in the sense of Aleksandrov. This generalizes a classical theorem by Shefel′ on saddle surfaces in 𝔼3.
Dimitrios E. Kalikakis
wiley +1 more source