| Title:
|
The Clairaut's theorem on rotational surfaces in pseudo-Euclidean 4-space with index 2 (English) |
| Author:
|
Almaz, Fatma |
| Author:
|
Külahci, Mihriban A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
63-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Clairaut’s theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the hyperbolic surfaces of rotation and the elliptic surface of rotation, respectively. (English) |
| Keyword:
|
Clairaut's theorem |
| Keyword:
|
surfaces of rotation |
| Keyword:
|
pseudo-Euclidean 4-space |
| Keyword:
|
geodesic curve |
| MSC:
|
53A35 |
| MSC:
|
53B30 |
| MSC:
|
53B50 |
| idZBL:
|
Zbl 08063787 |
| idMR:
|
MR4899031 |
| DOI:
|
10.14712/1213-7243.2025.001 |
| . |
| Date available:
|
2025-04-24T07:50:19Z |
| Last updated:
|
2026-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152945 |
| . |
| Reference:
|
[1] Almaz F., Külahcı M. A.: On $x$-magnetic surfaces generated by trajectory of $x$-magnetic curves in null cone.General Letters in Mathematics 5 (2018), no. 2, 84–92. 10.31559/glm2018.5.2.3 |
| Reference:
|
[2] Almaz F., Külahcı M. A.: A different interpretation on magnetic surfaces generated by special magnetic curve in $Q^{2}\subset E_{1}^{3}$.Adiyaman University Journal of Science 10 (2020), no. 2, 524–547. |
| Reference:
|
[3] Almaz F., Külahcı M. A.: The notes on rotational surfaces in Galilean space.Int. J. Geom. Methods Mod. Phys. 18 (2021), no. 2, Paper No. 2150017, 15 pages. MR 4209930, 10.1142/S0219887821500171 |
| Reference:
|
[4] Almaz F., Külahcı M. A.: A survey on tube surfaces in Galilean $3$-space.Journal of Polytechnic 25 (2022), no. 3, 1133–1142. |
| Reference:
|
[5] Almaz F., Külahcı M. A.: The research on rotational surfaces in pseudo Euclidean $4$-space with index $2$.Acta Math. Univ. Comenian. (N.S.) 92 (2023), no. 3, 263–279. MR 4650249 |
| Reference:
|
[6] Arnol'd V. I.: Mathematical Methods of Classical Mechanics.Graduate Texts in Mathematics, 60, Springer, New York, 1989. MR 0997295, 10.1007/978-1-4757-2063-1 |
| Reference:
|
[7] Ganchev G., Milousheva V.: General rotational surfaces in the $4$-dimensional Minkowski space.Turkish. J. Math. 38 (2014), no. 5, 883–895. MR 3225667, 10.3906/mat-1312-10 |
| Reference:
|
[8] Goemans W.: Flat double rotational surfaces in Euclidean and Lorentz–Minkowski $4$-space.Publ. Inst. Math. (Beograd) (N.S.) 103 (117) (2018), 61–68. MR 3812047, 10.2298/PIM1817061G |
| Reference:
|
[9] Hoffmann C. M., Zhou J.: Visualization of surfaces in four-dimensional space.Purdue University, Department of Computer Science Technical Reports (1990), Paper 814, 37 pages. |
| Reference:
|
[10] Lerner D.: Lie Derivatives, Isometries, and Killing Vectors.Lawrence, Kansas, Department of Mathematics, Univ. of Cansas, 2010. |
| Reference:
|
[11] Lugo G.: Differential Geometry in Physics.University of North Carolina Wilmington, UNCW, 2021. |
| Reference:
|
[12] Montiel S., Ros A.: Curves and Surfaces.Graduate Studies in Mathematics, 69, American Mathematical Society, Providence; Real Sociedad Matemática Española, Madrid, 2009. MR 2522595, 10.1090/gsm/069 |
| Reference:
|
[13] Pressley A.: Elementary Differential Geometry.Springer Undergraduate Mathematics Series, Springer, London, 2010. MR 2598317 |
| Reference:
|
[14] Shifrin T.: Differential Geometry: A First Course in Curves and Surfaces.Preliminary version, University of Georgia, 2011. MR 0726220 |
| Reference:
|
[15] Yaglom I. M.: A Simple Non-Euclidean Geometry and Its Physical Basis.Heidelberg Science Library, Springer, New York, 1979. MR 0520230 |
| . |
