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Journal articles on the topic 'Euclidean 4- space'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

İlarslan, Kazım, and Mehmet Yıldırım. "On Darboux helices in Euclidean 4‐space." Mathematical Methods in the Applied Sciences 42, no. 16 (2018): 5184–89. http://dx.doi.org/10.1002/mma.5260.

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12

Lyakhovets, Daniil Yu, and Alexander V. Osipov. "Some properties of topological hedgehogs." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 88 (2024): 37–52. http://dx.doi.org/10.17223/19988621/88/4.

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The topological spaces called Euclidean hedgehogs are considered. These are subspaces of the Euclidean spaces R n with the following property: together with each of their points, they contain the entire segment connecting the given point with the point of origin. It is proved that for all n ≥ 2 there exist pairwise non-homeomorphic Euclidean hedgehogs in Rn . It is also proved that for every countable Euclidean hedgehog there exists a flat hedgehog homeomorphic to it. We also consider two topological spaces: the quasimetric hedgehog and the quotient hedgehog, which have the following cardinal

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13

Schaeben, H. "“Normal” Orientation Distributions." Textures and Microstructures 19, no. 4 (1992): 197–202. http://dx.doi.org/10.1155/tsm.19.197.

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Analogues of the normal distribution in Euclidean space for orientations represented by Rodrigues parameters are discussed. It is emphasized that different characterizations of the normal distribution in Euclidean space lead to different distributions in other spaces, none of which is mathematically superior to any other one. Particular analogues of the normal distribution are the Bingham distribution on S+4 for the purposes of mathematical statistics, and the Brownian motion distribution on S+4 in terms of probability theory and stochastic processes. It is reminded of the fact that a simple a

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14

TUNÇ, Emrah, and Bengü BAYRAM. "A New Characterization of Tzitzeica Curves in Euclidean 4-Space." Fundamentals of Contemporary Mathematical Sciences 4, no. 2 (2023): 77–86. http://dx.doi.org/10.54974/fcmathsci.1176710.

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In this study, we are interested in Tzitzeica curves (Tz-curves) in Euclidean 4 -space. Tz-curve condition for Euclidean 4 -space are determined as three types for three hyperplanes and some examples are given.

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15

Abe, K., and D. E. Blair. "Ruled hypersurfaces of Euclidean space." Rocky Mountain Journal of Mathematics 17, no. 4 (1987): 697–708. http://dx.doi.org/10.1216/rmj-1987-17-4-697.

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16

Aiyama, Reiko, and Kazuo Akutagawa. "Semiumbilic points for minimal surfaces in Euclidean $$4$$ 4 -space." Geometriae Dedicata 170, no. 1 (2013): 1–7. http://dx.doi.org/10.1007/s10711-013-9865-y.

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17

Maciocia, Antony. "Metrics on the moduli spaces of instantons over Euclidean 4-space." Communications in Mathematical Physics 135, no. 3 (1991): 467–82. http://dx.doi.org/10.1007/bf02104116.

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18

Aiyama, Reiko, and Kazuo Akutagawa. "Surfaces with inflection points in Euclidean 4-space." Kodai Mathematical Journal 37, no. 1 (2014): 174–86. http://dx.doi.org/10.2996/kmj/1396008253.

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19

Yoon, Dae Won, Yilmaz Tuncer, and Murat Kemal Karacan. "Generalized Mannheim quaternionic curves in Euclidean 4-space." Applied Mathematical Sciences 7 (2013): 6583–92. http://dx.doi.org/10.12988/ams.2013.310560.

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20

Peng, ChiaKuei, and ZiZhou Tang. "On surfaces immersed in Euclidean space R 4." Science in China Series A: Mathematics 53, no. 1 (2010): 251–56. http://dx.doi.org/10.1007/s11425-010-0004-z.

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21

Arslan, Kadri, Bengü Bayram, Betül Bulca, and Günay Öztürk. "On translation surfaces in 4-dimensional Euclidean space." Acta et Commentationes Universitatis Tartuensis de Mathematica 20, no. 2 (2016): 123. http://dx.doi.org/10.12697/acutm.2016.20.11.

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22

Nawratil, Georg. "Fundamentals of Quaternionic Kinematics in Euclidean 4-Space." Advances in Applied Clifford Algebras 26, no. 2 (2015): 693–717. http://dx.doi.org/10.1007/s00006-015-0613-2.

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23

Yeğin Şen, Rüya, and Nurettin Cenk Turgay. "On biconservative surfaces in 4-dimensional Euclidean space." Journal of Mathematical Analysis and Applications 460, no. 2 (2018): 565–81. http://dx.doi.org/10.1016/j.jmaa.2017.12.009.

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24

Mori, Hiroshi, and Norio Shimakura. "Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing normal curvature." Tohoku Mathematical Journal 61, no. 4 (2009): 523–50. http://dx.doi.org/10.2748/tmj/1264084498.

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25

Li, Yanlin, Ali Uçum, Kazım İlarslan, and Çetin Camcı. "A New Class of Bertrand Curves in Euclidean 4-Space." Symmetry 14, no. 6 (2022): 1191. http://dx.doi.org/10.3390/sym14061191.

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Bertrand curves are a pair of curves that have a common principal normal vector at any point and are related to symmetry properties. In the present paper, we define the notion of 1,3-V Bertrand curves in Euclidean 4-space. Then we find the necessary and sufficient conditions for curves in Euclidean 4-space to be 1,3-V Bertrand curves. Some related examples are given.

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26

Diop, Oumar, and Ameth Ndiaye. "Geometry of hypersurfaces in Euclidean 4-space with Caputo fractional derivatives." Journal of Interdisciplinary Mathematics 28, no. 4 (2025): 1367–84. https://doi.org/10.47974/jim-1794.

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The aim of this paper is to generalize the paper in [7] in 4-dimensional Euclidean space. We define and calculate the geometries of hypersurface in an Euclidean four space using the Caputo fractional derivative. Using the fractional calculus we give the geometrics of the considered hypersurface. We give some example using the graphs of some functions in ℝ3.

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27

Ganchev, Georgi, and Velichka Milousheva. "Surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space." Filomat 33, no. 4 (2019): 1135–45. http://dx.doi.org/10.2298/fil1904135g.

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We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three invariant functions. We prove that any surface with parallel normalized mean curvature vector field parametrized by canonical parameters is determined uniquely up to a motion in Euclidean (or Minkowski) space by the three invariant functions satisfying a system of three partial differential equations. We find examples of surfaces with parallel normalized mean

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28

Pashaie, Firooz. "On $L_1$-biharmonic timelike hypersurfaces in pseudo-Euclidean space $E_1^4$." Tamkang Journal of Mathematics 51, no. 4 (2020): 313–32. http://dx.doi.org/10.5556/j.tkjm.51.2020.3188.

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A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3\rightarrow\E_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen'

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29

BÜYÜKKÜTÜK, Sezgin, and Günay ÖZTÜRK. "A Characterization of Factorable Surfaces in Euclidean 4-Space E^4." Kocaeli Journal of Science and Engineering 1, no. 1 (2018): 15–20. http://dx.doi.org/10.34088/kojose.403665.

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30

McKEON, D. G. C., and T. N. SHERRY. "GAUGE MODEL WITH EXTENDED FIELD TRANSFORMATIONS IN EUCLIDEAN SPACE." International Journal of Modern Physics A 15, no. 02 (2000): 227–50. http://dx.doi.org/10.1142/s0217751x00000100.

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An SO(4) gauge-invariant model with extended field transformations is examined in four-dimensional Euclidean space. The gauge field is (Aμ)αβ=½tμνλ(Mνλ)αβ where Mνλ are the SO(4) generators in the fundamental representation. The SO(4) gauge indices also participate in the Euclidean space SO(4) transformations giving the extended field transformations. We provide the decomposition of the reducible field tμνλ in terms of fields irreducible under SO(4). The SO(4) gauge transformations for the irreducible fields mix fields of different spin. Reducible matter fields are introduced in the form of a

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31

Schmerl, James H. "Avoidable algebraic subsets of Euclidean space." Transactions of the American Mathematical Society 352, no. 6 (1999): 2479–89. http://dx.doi.org/10.1090/s0002-9947-99-02331-4.

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32

Stainsby, S. J., and R. T. Cahill. "Is space-time euclidean “inside” hadrons?" Physics Letters A 146, no. 9 (1990): 467–70. http://dx.doi.org/10.1016/0375-9601(90)90387-4.

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33

ARSLAN, KADRI, ALIM SUTVEREN та BETUL BULCA. "Rotational λ – hypersurfaces in Euclidean spaces". Creative Mathematics and Informatics 30, № 1 (2021): 29–40. http://dx.doi.org/10.37193/cmi.2021.01.04.

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Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, \lambda -hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider \lambda -hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4-space \mathbb{R}^{4} to become self-shrinkers. Furthermore, we classify the general rotational \lambda -hypersurfaces with constant mean curvature. As an application, we give some

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34

YENEROĞLU, MUSTAFA, and AHMET DUYAN. "ASSOCIATED CURVES ACCORDING TO BISHOP FRAME IN 4-DIMENSIONAL EUCLIDEAN SPACE." Journal of Science and Arts 24, no. 1 (2024): 105–10. http://dx.doi.org/10.46939/j.sci.arts-24.1-a09.

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Many studies have been doneaccording to different frames of the theory of curves in Euclidean Space. Many scientists have studied frames such as the Frenet frame, Bishop frame, and Adapted frame in this theory. These frames help us in the characterization of curves.In this study, associated curves with the Frenet curve according to the Bishop frame in 4-dimensional Euclidean space are investigated. Direction and rectifying curves of the Frenet curve according to this frame are given.

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35

ISHIKAWA, Susumu. "BIHARMONIC W-SURFACES IN 4-DIMENSIONAL PSEUDO-EUCLIDEAN SPACE." Memoirs of the Faculty of Science, Kyusyu University. Series A, Mathematics 46, no. 2 (1992): 269–86. http://dx.doi.org/10.2206/kyushumfs.46.269.

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36

Iqbal, Zafar, and Joydeep Sengupta. "On f-rectifying curves in the Euclidean 4-space." Acta Universitatis Sapientiae, Mathematica 13, no. 1 (2021): 192–208. http://dx.doi.org/10.2478/ausm-2021-0011.

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Abstract A rectifying curve in the Euclidean 4-space 𝔼4 is defined as an arc length parametrized curve γ in 𝔼4 such that its position vector always lies in its rectifying space (i.e., the orthogonal complement Nγ ˔ of its principal normal vector field Nγ) in 𝔼4. In this paper, we introduce the notion of an f-rectifying curve in 𝔼4 as a curve γ in 𝔼4 parametrized by its arc length s such that its f-position vector γf, defined by γf (s) = ∫ f(s)dγ for all s, always lies in its rectifying space in 𝔼4, where f is a nowhere vanishing integrable function in parameter s of the curve γ. Also, we chara

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37

Yoon, Dae-Won. "ON THE QUATERNIONIC GENERAL HELICES IN EUCLIDEAN 4-SPACE." Honam Mathematical Journal 34, no. 3 (2012): 381–90. http://dx.doi.org/10.5831/hmj.2012.34.3.381.

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38

Kido, Hiroaki. "On Isosceles Sets in the 4-Dimensional Euclidean Space." International Journal of Combinatorics 2010 (January 9, 2010): 1–30. http://dx.doi.org/10.1155/2010/803210.

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A subset in the -dimensional Euclidean space that contains points (elements) is called an -point isosceles set if every triplet of points selected from them forms an isosceles triangle. In this paper, we show that there exist exactly two 11-point isosceles sets in up to isomorphisms and that the maximum cardinality of isosceles sets in is 11.

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39

Rippon, P. J. "Asymptotic values of continuous functions in Euclidean space." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 2 (1992): 309–18. http://dx.doi.org/10.1017/s030500410007540x.

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40

Yang, Li Jun, and Xian Wu Zeng. "Two Characterizations of Diffeomorphisms of Euclidean Space." Acta Mathematica Sinica, English Series 19, no. 4 (2003): 739–44. http://dx.doi.org/10.1007/s10114-002-0232-4.

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41

Montaldo, S., C. Oniciuc, and A. Ratto. "Proper biconservative immersions into the Euclidean space." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 2 (2014): 403–22. http://dx.doi.org/10.1007/s10231-014-0469-4.

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42

FAVER, TIMOTHY, KATELYNN KOCHALSKI, MATHAV KISHORE MURUGAN, HEIDI VERHEGGEN, ELIZABETH WESSON, and ANTHONY WESTON. "ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES." Glasgow Mathematical Journal 56, no. 3 (2013): 519–35. http://dx.doi.org/10.1017/s0017089513000438.

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AbstractMotivated by a classical theorem of Schoenberg, we prove that an n + 1 point finite metric space has strict 2-negative type if and only if it can be isometrically embedded in the Euclidean space $\mathbb{R}^{n}$ of dimension n but it cannot be isometrically embedded in any Euclidean space $\mathbb{R}^{r}$ of dimension r < n. We use this result as a technical tool to study ‘roundness’ properties of additive metrics with a particular focus on ultrametrics and leaf metrics. The following conditions are shown to be equivalent for a metric space (X,d): (1) X is ultrametric, (2) X has inf

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43

Baškienė, Angelė. "Hyperbolic normal almost contactmetric hypersurfaces in Euclidean 4-dimensional space." Lietuvos matematikos rinkinys 45 (December 18, 2005): 89–92. http://dx.doi.org/10.15388/lmr.2005.24560.

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44

RANJBAR, HASSAN, and ASADOLLAH NIKNAM. "FURTHER INEQUALITIES FOR THE EUCLIDEAN OPERATOR RADIUS." Journal of Inequalities and Special Functions 12, no. 4 (2021): 25–32. http://dx.doi.org/10.54379/jiasf-2021-4-3.

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By use of some non-negative Hermitian forms defined for n-tuple of bounded linear operators on the Hilbert space (H, h·, ·i) we establish new numerical radius and operator norm inequalities for sum of products of operators

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45

Dranishnikov, A. N. "On intersections of compacta in Euclidean space." Proceedings of the American Mathematical Society 112, no. 1 (1991): 267. http://dx.doi.org/10.1090/s0002-9939-1991-1042264-4.

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46

Wan-yun, Zhao. "Finite Temperature Axial Anomaly in Euclidean Space." Communications in Theoretical Physics 4, no. 2 (1985): 219–51. http://dx.doi.org/10.1088/0253-6102/4/2/219.

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47

Kula, L., and Y. Yayli. "HOMOTHETIC MOTIONS IN SEMI-EUCLIDEAN SPACE $\mathbb{E}_2^4 $." Mathematical Proceedings of the Royal Irish Academy 105A, no. 1 (2005): 9–15. http://dx.doi.org/10.1353/mpr.2005.0016.

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48

Kocayigit, Huseyin, and Zennure Cicek. "Some characterizations of constant breadth curves in Euclidean 4-space." New Trends in Mathematical Science 4, no. 1 (2016): 214. http://dx.doi.org/10.20852/ntmsci.2016115856.

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49

Badr, Sayed Abdel-Naeim, Nassar H. Abdel-All, Osmar Aléssio, Mustafa Düldül, and Bahar Uyar Düldül. "Non-transversal intersection curves of hypersurfaces in Euclidean 4-space." Journal of Computational and Applied Mathematics 288 (November 2015): 81–98. http://dx.doi.org/10.1016/j.cam.2015.03.054.

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50

Defever, Filip, George Kaimakamis, and Vassilis Papantoniou. "Biharmonic hypersurfaces of the 4-dimensional semi-Euclidean space Es4." Journal of Mathematical Analysis and Applications 315, no. 1 (2006): 276–86. http://dx.doi.org/10.1016/j.jmaa.2005.05.049.

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