Relevant bibliographies by topics / Euclidean 4- space

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Euclidean 4- space'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Euclidean 4- space"

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Hashimoto, Hideya. "Hypersurfaces in 4-dimensional Euclidean space." Czechoslovak Mathematical Journal 40, no. 2 (1990): 315–24. http://dx.doi.org/10.21136/cmj.1990.102383.

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Crabb, M. C. "Immersing projective spaces in Euclidean space." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 117, no. 1-2 (1991): 155–70. http://dx.doi.org/10.1017/s0308210500027670.

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SynopsisUsing the KOℝ/2-theoretic obstruction theory developed in [4] and [5], necessary and sufficient conditions are derived for quaternionic projective spaces ℍPk and odd-dimensional complex projective spaces ℂP2k+1, of real dimension m say, to immerse in Euclidean space ℝ2m−1 in the range l ≦ 14. The results refine those obtained by Davis and Mahowald ([10, 11]) and earlier authors.
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DESHMUKH, Sharief, İbrahim AL-DAYEL, and Kazım İLARSLAN. "Frenet Curves in Euclidean 4-Space." International Electronic Journal of Geometry 10, no. 2 (2017): 56–66. http://dx.doi.org/10.36890/iejg.545050.

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Elzawy, Mervat. "Smarandache curves in Euclidean 4- space E 4." Journal of the Egyptian Mathematical Society 25, no. 3 (2017): 268–71. http://dx.doi.org/10.1016/j.joems.2017.03.003.

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Suyama, Yoshihiko. "Conformally flat hypersurfaces in Euclidean 4-space." Nagoya Mathematical Journal 158 (December 2000): 1–42. http://dx.doi.org/10.1017/s0027763000007273.

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AbstractWe study generic and conformally flat hypersurfaces in Euclidean four-space. What kind of conformally flat three manifolds are really immersed generically and conformally in Euclidean space as hypersurfaces? According to the theorem due to Cartan [1], there exists an orthogonal curvature-line coordinate system at each point of such hypersurfaces. This fact is the first step of our study. We classify such hypersurfaces in terms of the first fundamental form. In this paper, we consider hypersurfaces with the first fundamental forms of certain specific types. Then, we give a precise repre
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Kazan, Ahmet, Mustafa Altın, and Dae Yoon. "Geometric characterizations of canal hypersurfaces in Euclidean spaces." Filomat 37, no. 18 (2023): 5909–20. http://dx.doi.org/10.2298/fil2318909k.

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In the present paper, firstly we obtain the general expression of canal hypersurfaces in Euclidean n-space and deal with canal hypersurfaces in Euclidean 4-space E4. We compute Gauss map, Gaussian curvature and mean curvature of canal hypersurfaces in E4 and obtain an important relation between the mean and Gaussian curvatures as 3H? = K?3 ? 2. We prove that, the flat canal hypersurfaces in Euclidean 4-space are only circular hypercylinders or circular hypercones and minimal canal hypersurfaces are only generalized catenoids. Also, we state the expression of tubular hypersurfaces in Euclidean
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Altın, Mustafa, Ahmet Kazan, and Dae Won Yoon. "2-Ruled hypersurfaces in Euclidean 4-space." Journal of Geometry and Physics 166 (August 2021): 104236. http://dx.doi.org/10.1016/j.geomphys.2021.104236.

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Bulca, Betül, Kadri Arslan, Bengü Bayram, and Günay Öztürk. "Canal surfaces in 4-dimensional Euclidean space." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7, no. 1 (2016): 83–89. http://dx.doi.org/10.11121/ijocta.01.2017.00338.

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In the present study, we consider canal surfaces imbedded in an Euclidean space of four dimensions. The curvature properties of these surface are investigated with respect to the variation of the normal vectors and curvature ellipse. We also give some special examples of canal surfaces in E^4. Further, we give necessary and sufficient condition for canal surfaces in E^4 to become superconformal. Finally, the visualization of the projections of canal surfaces in E^3 are presented.
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Chen, Bang-Yen. "On ideal hypersurfaces of Euclidean 4-space." Arab Journal of Mathematical Sciences 19, no. 2 (2013): 129–44. http://dx.doi.org/10.1016/j.ajmsc.2013.05.001.

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Bulca, Betul, та Kadri Arslan. "Surface pencils in Euclidean 4-space 𝔼4". Asian-European Journal of Mathematics 09, № 04 (2016): 1650074. http://dx.doi.org/10.1142/s1793557116500741.

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In this paper, we study the problem of constructing a family of surfaces (surface pencils) from a given curve in [Formula: see text]-dimensional Euclidean space [Formula: see text]. We have shown that the generalized rotation surfaces in [Formula: see text] are the special type of surface pencils. Further, the curvature properties of these surfaces are investigated. Finally, we give some examples of flat surface pencils in [Formula: see text].
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Dissertations / Theses on the topic "Euclidean 4- space"

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Targino, Renato Oliveira. "A Curvatura de Gauss-Kronecker de hipersuperfÃcies mÃnimas em formas espaciais 4-dimensionais." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6672.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Neste trabalho estudamos hipersuperfÃcies mÃnimas completas e com curvatura de Gauss-Kronecker constante em uma forma espacial Q4(c). Provamos que o Ãnfimo do valor absoluto da curvatura de Gauss-Kronecker de uma hipersuperfÃcie mÃnima completa em Q4(c); c &#8804; 0; na qual a curvatura de Ricci à limitado inferiormente, à igual a zero. AlÃm disso, estudamos hipersuperfÃcies mÃnimas conexas M3 em uma forma espacial Q4(c) com curvatura de Gauss-Kronecker K constante. Para o caso c &#8804; 0, provamos, por um argumento local, que se
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Books on the topic "Euclidean 4- space"

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Uchiyama, Akihito. Hardy Spaces on the Euclidean Space. Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67905-9.

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Müller, Claus. Analysis of Spherical Symmetries in Euclidean Spaces. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0581-4.

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Mass.) AMS Special Session on Radon Transforms and Geometric Analysis (2012 Boston. Geometric analysis and integral geometry: AMS special session in honor of Sigurdur Helgason's 85th birthday, radon transforms and geometric analysis, January 4-7, 2012, Boston, MA ; Tufts University Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces, January 8-9, 2012, Medford, MA. Edited by Quinto, Eric Todd, 1951- editor of compilation, Gonzalez, Fulton, 1956- editor of compilation, Christensen, Jens Gerlach, 1975- editor of compilation, and Tufts University. Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces. American Mathematical Society, 2013.

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Behrens, Stefan, Boldizsar Kalmar, Min Hoon Kim, Mark Powell, and Arunima Ray, eds. The Disc Embedding Theorem. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198841319.001.0001.

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The disc embedding theorem provides a detailed proof of the eponymous theorem in 4-manifold topology. The theorem, due to Michael Freedman, underpins virtually all of our understanding of 4-manifolds in the topological category. Most famously, this includes the 4-dimensional topological Poincaré conjecture. Combined with the concurrent work of Simon Donaldson, the theorem reveals a remarkable disparity between the topological and smooth categories for 4-manifolds. A thorough exposition of Freedman’s proof of the disc embedding theorem is given, with many new details. A self-contained account o
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Mercati, Flavio. Best Matching: Technical Details. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0005.

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The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The cha
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Book chapters on the topic "Euclidean 4- space"

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Kharazishvili, Alexander. "Isosceles triangles and it-sets in Euclidean space." In Introduction to Combinatorial Methods in Geometry. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003458708-4.

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Nikolov, Nikolay M., Raymond Stora, and Ivan Todorov. "Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly." In Lie Theory and Its Applications in Physics. Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54270-4_9.

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d'Alessandro, Paolo. "Linear Optimization Problems in Euclidean Spaces." In Conical Approach to Linear Programming. CRC Press, 2024. https://doi.org/10.1201/9781003580614-4.

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Zhiyong, Zheng, Liu Fengxia, Lu Yunfan, and Tian Kun. "Cyclic Lattices, Ideal Lattices, and Bounds for the Smoothing Parameter." In Financial Mathematics and Fintech. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-2366-3_7.

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AbstractCyclic lattices and ideal lattices were introduced by Micciancio (2002), Lyubashevsky and Micciancio (2006), respectively, which play an efficient role in Ajtai’s construction of a collision resistant Hash function (see Ajtai (1996), Ajtai and Dwork (1997)) and in Gentry’s construction of fully homomorphic encryption (see Gentry (2009)). Let $$R=Z[x]/\langle \phi (x)\rangle $$ R = Z [ x ] / ⟨ ϕ ( x ) ⟩ be a quotient ring of the integer coefficients polynomials ring, Lyubashevsky and Micciancio regarded an ideal lattice as the correspondence of an ideal of R, but they neither explain ho
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Yamaguti, Masaya, Louis Nirenberg, Sigeru Mizohata, and Yasutaka Sibuya. "A note on the theory of degree of mapping in Euclidean spaces." In Mitio Nagumo Collected Papers. Springer Japan, 1993. http://dx.doi.org/10.1007/978-4-431-68222-6_39.

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"Three-Dimensional Euclidean Space R3." In Geomathematically Oriented Potential Theory. Chapman and Hall/CRC, 2012. http://dx.doi.org/10.1201/b13057-4.

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"Surfaces in the Euclidean 4-space." In Differential Geometry from a Singularity Theory Viewpoint. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814590457_0007.

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Snygg, John. "Clifford Algebra For Flat n-Dimensional Spaces." In Clifford Algebra. Oxford University PressNew York, NY, 1997. http://dx.doi.org/10.1093/oso/9780195098242.003.0003.

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Abstract In Chapter 1, we dealt with Clifford numbers in Euclidean 3-space. In Chapter 2, we dealt with Clifford numbers in Minkowski 4-space. This chapter is devoted to showing how these notions can be extended to “flat” spaces of any finite dimension.
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Zhizhin, G. V., and M. V. Diudea. "Space of Nanoworld." In Sustainable Nanosystems Development, Properties, and Applications. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-0492-4.ch007.

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In this chapter, a geometrical model to accurately describe the distribution of light points in diffraction patterns of quasicrystals is proposed. It is shown that the proposed system of parallel lines has axes of the fifth order, periodically repeating the fundamental domain of the quasicrystals. A 4D- polytope, called the golden hyperrombohedron is introduced. It consists from eight rhombohedrons densely filling the 4D space (like the regular 8-Cell). Faces of the hyperrombohedron are connected by the golden section; they can be scaled as needed. On this universal lattice of the golden hyper
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Challal, Samia. "Constrained Optimization-Inequality Constraints." In Introduction to the Theory of Optimization in Euclidean Space. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429203152-4.

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Conference papers on the topic "Euclidean 4- space"

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Watanabe, Yoko, Sylvain Dessus, and Patrick Fabiani. "Safe Path Planning with Localization Uncertainty for Urban Operation of VTOL UAV." In Vertical Flight Society 70th Annual Forum & Technology Display. The Vertical Flight Society, 2014. http://dx.doi.org/10.4050/f-0070-2014-9673.

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This paper proposes a safe 3D path planner for an urban operation of VTOL-type UAV. One of the difficulties of navigating an UAV in an urban environment involves its degraded self-localization accuracy due to GPS signal occlusion. In order to keep UAV navigability in such a GPS-denied area, alternative navigation systems (mostly using visual sensing) have been proposed in many literatures. This paper suggests incorporating different means of self-localization and their position-dependent availabilities in path planning task. Localization uncertainty corridor is defined by a space swept by the
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Kahraman Aksoyak, Ferdağ, and Yusuf Yaylı. "Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo Euclidean Space $\mathbb{E}_{2}^{4}$." In International Workshop on Theory of Submanifolds 2016. Istanbul Teknik Üniversitesi, 2017. http://dx.doi.org/10.24064/iwts2016.2017.13.

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Purwar, Anurag, and Q. J. Ge. "Polar Decomposition of Unit Dual Quaternions." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70882.

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This paper seeks to extend the notion of polar decomposition from matrix algebra to dual quaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the polar decompositions (PD) of spatial displacements in Euclidean three-space that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigid-body displacements. It is shown in this paper that a dual quaternion representing an element of
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Ge, Q. J. "On the Matrix Algebra Realization of the Theory of Biquaternions." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0221.

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Abstract This paper describes a matrix algebra presentation of Clifford’s theory of biquaternions. We examine 4 × 4 skew-symmetric matrices and use their exponentials to relate quaternions to equal-angle double rotations in Euclidean four-space E4. We show how double rotations in E4 expressed in terms of plane coordinates lead to elliptic biquaternions in both Plücker and Study forms and present the fundamental Plücker and Study conditions that govern the biquaternions. Finally, we show that a spatial displacement in E3 in terms of parabolic biquaternions (or dual quaternions) is a limiting ca
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Bru¨ls, Olivier, Martin Arnold, and Alberto Cardona. "Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48132.

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This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the n
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Polat, Gülistan, Bayram Şahin, and Jae Won Lee. "Inequalities for Riemannian Submersions Involving Casorati Curvatures: A New Approach." In 6th International Students Science Congress. Izmir International Guest Student Association, 2022. http://dx.doi.org/10.52460/issc.2022.031.

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For surfaces in a Euclidean 3-space Casorati [4] introduced a new curvature in 1890 what is today called the Casorati curvature. This curvature was preferred by Casorati over Gauss curvature because Gauss curvature may vanish for surfaces that look intuitively curved, while Casorati curvature only vanishes at the planer points. The Casorati curvature C of submanifolds in a Riemannian manifold is the extrinsic invariant given by the normalized square of the second fundamental form and some optimal inequalities containing Casorati curvatures were obtained for submanifolds of real space forms, co
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Husty, Manfred L., Martin Pfurner, and Hans-Peter Schro¨cker. "A New and Efficient Algorithm for the Inverse Kinematics of a General Serial 6R." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84745.

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In this paper a new and very efficient algorithm to compute the inverse kinematics of a general 6R serial kinematic chain is presented. The main idea is to make use of classical multidimensional geometry to structure the problem and to use the geometric information before starting the elimination process. For the geometric preprocessing we use the Study model of Euclidean displacements, sometimes called kinematic image, which identifies a displacement with a point on a six dimensional quadric S62 in seven dimensional projective space P7. The 6R chain is broken up in the middle to form two open
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Taylor, Laurence R. "Smooth Euclidean 4–spaces with few symmetries." In Low Dimensional Topology -- The Kirbyfest. Mathematical Sciences Publishers, 1999. http://dx.doi.org/10.2140/gtm.1999.2.563.

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Ge, Qiaode Jeffrey, Zihan Yu, Mona Arbab, and Mark Langer. "On the Computation of the Average of Spatial Displacements." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-90156.

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Abstract Many applications in biomechanics and medical imaging call for the analysis of the kinematic errors in a group of patients statistically using the average displacement and the standard deviations from the average. This paper studies the problem of computing the average displacement from a set of given spatial displacements using three types of parametric representations: Euler angles and translation vectors, unit quaternions and translation vectors, and dual quaternions. It has been shown that the use of Euclidean norm in the space of unit quaternions reduces the problem to that of co
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Lall, Pradeep, Peter Sakalaukus, and Lynn Davis. "An Investigation of Catastrophic Failure in Solid-State Lamps Exposed to Harsh Environment Operational Conditions." In ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems collocated with the ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ipack2015-48257.

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Today’s lighting technology is steadily becoming more energy efficient and less toxic to the environment since the passing of the Energy Independence and Security Act of 2007 (EISA) [1]. EISA has mandated a higher energy efficiency standard for lighting products and the phase out of the common incandescent lamp. This has led lighting manufacturers to pursue solid-state lighting (SSL) technologies for consumer lighting applications. However, two major roadblocks are hindering the transition process to SSL lamps: cost and quality. In order to cut cost, manufactures are moving towards cheaper pac
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