KaydedilenlerDerginizi ekleyin

Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 2

Timelike rotational hypersurfaces with timelike axis in Minkowski four-space

Erhan Güler(BARTIN UNIVERSITY)0000-0003-3264-6239
Sayfa
—
Yayın Tarihi
2023-06-23
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we present a theorem for the rotational hypersurfaces with timelike axis supplying $\Delta\textbf{x}=\mathcal{T}\textbf{x}$, where $\mathcal{T}$ is a 4x4 real matrix.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We introduce the timelike rotational hypersurfaces $\textbf{x}$ with timelike axis in Minkowski 4-space $\mathbb{E}_1^{4}$.
📊
Temel Bulgular & Veri:We obtain the equations for the curvatures of the hypersurface.
💡
Sonuç & Katkı:Moreover, we present a theorem for the rotational hypersurfaces with timelike axis supplying $\Delta\textbf{x}=\mathcal{T}\textbf{x}$, where $\mathcal{T}$ is a 4x4 real matrix.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rotational hypersurface · timelike axis · Laplace-Beltrami operator

Abstract

We introduce the timelike rotational hypersurfaces $\textbf{x}$ with timelike axis in Minkowski 4-space $\mathbb{E}_1^{4}$. We obtain the equations for the curvatures of the hypersurface. Moreover, we present a theorem for the rotational hypersurfaces with timelike axis supplying $\Delta\textbf{x}=\mathcal{T}\textbf{x}$, where $\mathcal{T}$ is a 4x4 real matrix.

🔖

Bu Makaleye Atıf Yap

Güler, E. (2023). Timelike rotational hypersurfaces with timelike axis in Minkowski four-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 2. https://doi.org/10.31801/cfsuasmas.1062426

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (30)

  1. Arslan, K., Bayram, B. K., Bulca, B., Öztürk, G., Generalized rotation surfaces in $E^{4}$, Results Math., 61(3) (2012), 315–327. https://doi.org/10.1007/s00025-011-0103-3
  2. Arslan, K., Deszcz, R., Yaprak, S¸., On Weyl pseudosymmetric hypersurfaces, Colloq. Math., 72(2) (1997), 353–361.
  3. Arslan, K., Milousheva, V., Meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map in Minkowski 4-space, Taiwanese J. Math., 20(2) (2016), 311–332. https://doi.org/10.11650/tjm.19.2015.5722
  4. Arvanitoyeorgos, A., Kaimakamis, G., Magid, M., Lorentz hypersurfaces in $E_{1}^{4}$ satisfying $\Delta H=\alpha H,$ Illinois J. Math., 53(2) (2009), 581–590. https://doi.org/10.1215/ijm/1266934794
  5. Beneki, Chr. C., Kaimakamis, G., Papantoniou, B. J., Helicoidal surfaces in three-dimensional Minkowski space, J. Math. Anal. Appl., 275 (2002), 586–614. https://doi.org/10.1016/S0022-247X(02)00269-X
  6. Chen, B. Y., Total Mean Curvature and Submanifolds of Finite Type, 2nd Ed., World Scientific, Singapore, 2014. https://doi.org/10.1142/9237
  7. Cheng, Q. M., Wan, Q. R., Complete hypersurfaces of $R^{4}$ with constant mean curvature, Monatsh. Math., 118 (1994), 171–204. https://doi.org/10.1007/BF01301688
  8. Cheng, S. Y., Yau, S. T., Hypersurfaces with constant scalar curvature, Math. Ann., 225 (1977), 195–204. https://doi.org/10.1007/BF01425237
  9. Dillen, F., Fastenakels, J., Van der Veken, J., Rotation hypersurfaces of $S^{n}×R$ and $H^{n}×R,$ Note Mat., 29(1) (2009), 41–54. https://doi.org/10.1285/i15900932v29n1p41
  10. Do Carmo, M. P., Dajczer, M., Rotation hypersurfaces in spaces of constant curvature, Trans. Am. Math. Soc., 277 (1983), 685–709. https://doi.org/10.1007/978-3-642-25588-517
  11. Dursun, U., Hypersurfaces with pointwise 1-type Gauss map, Taiwanese J. Math., 11(5) (2007), 1407–1416. https://doi.org/10.11650/twjm/1500404873
  12. Dursun, U., Turgay, N. C., Space-like surfaces in Minkowski space $E_{1}^{4}$ with pointwise 1-type Gauss map, Ukr. Math. J., 71(1) (2019), 64–80. https://doi.org/10.1007/s11253-019-01625-8
  13. Ferrandez, A., Garay, O. J., Lucas, P., On a certain class of conformally flat Euclidean hypersurfaces, In Global Differential Geometry and Global Analysis, Lecture Notes in Mathematics, vol 1481. Springer, Heidelberg, Berlin, Germany, 1991, 48–54. https://doi.org/10.1007/BFb0083627
  14. Ganchev, G., Milousheva, V., General rotational surfaces in the 4-dimensional Minkowski space, Turkish J. Math., 38 (2014), 883–895. https://doi.org/10.3906/mat-1312-10
  15. Güler, E., Helical hypersurfaces in Minkowski geometry $E_{1}^{4}$, Symmetry, 12(8) (2020), 1–16. https://doi.org/10.3390/sym12081206
  16. Güler, E., Fundamental form IV and curvature formulas of the hypersphere, Malaya J. Mat., 8(4) (2020), 2008–2011. https://doi.org/10.26637/MJM0804/0116
  17. Güler, E., Rotational hypersurfaces satisfying $\Delta ^{I}R = AR$ in the four-dimensional Euclidean space, J. Polytech., 24(2) (2021), 517–520. https://doi.org/10.2339/politeknik.670333
  18. Güler, E., Hacısalihoglu, H. H., Kim, Y.H., The Gauss map and the third Laplace–Beltrami operator of the rotational hypersurface in 4-space, Symmetry, 10(9) (2018), 1–12. https://doi.org/10.3390/sym10090398
  19. Güler, E., Magid, M., Yaylı, Y., Laplace–Beltrami operator of a helicoidal hypersurface in four-space, J. Geom. Symmetry Phys., 41 (2016), 77–95. https://doi.org/10.7546/jgsp-41-2016-77-95
  20. Güler, E., Turgay, N. C., Cheng–Yau operator and Gauss map of rotational hypersurfaces in 4-space, Mediterr. J. Math., 16(3) (2019), 1–16. https://doi.org/10.1007/s00009-019-1333-y
  21. Hasanis, Th., Vlachos, Th., Hypersurfaces in $E^{4} with harmonic mean curvature vector field, Math. Nachr., 172 (1995), 145–169. https://doi.org/10.1002/mana.19951720112
  22. Kim, Y. H., Turgay, N. C., Surfaces in $E^{4}$ with $L_{1}$-pointwise 1-type Gauss map, Bull. Korean Math. Soc., 50(3) (2013), 935–949. http://dx.doi.org/10.4134/BKMS.2013.50.3.935
  23. Lawson, H. B., Lectures on Minimal Submanifolds, Vol. I., Second ed., Mathematics Lecture Series, 9. Publish or Perish, Wilmington, Del., 1980.
  24. Magid, M., Scharlach, C., Vrancken, L., Affine umbilical surfaces in R4, Manuscripta Math., 88 (1995), 275–289. http://dx.doi.org/10.1007/BF02567823
  25. Moore, C., Surfaces of rotation in a space of four dimensions, Ann. Math., 21 (1919), 81–93. https://doi.org/10.2307/2007223
  26. Moore, C., Rotation surfaces of constant curvature in space of four dimensions, Bull. Amer. Math. Soc., 26 (1920), 454–460. https://doi.org/10.1090/S0002-9904-1920-03336-7
  27. O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  28. Takahashi, T., Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18 (1966), 380–385. https://doi.org/10.2969/jmsj/01840380
  29. Turgay, N. C., Upadhyay, A., On biconservative hypersurfaces in 4-dimensional Riemannian space forms, Math. Nachr., 292(4) (2019), 905–921. https://doi.org/10.1002/mana.201700328
  30. Arvanitoyeorgos, A., Kaimakamis, G., Magid, M., Lorentz hypersurfaces in $E_{1}^{4}$ satisfying $\Delta H=\alpha H,$ Illinois J. Math., 53(2) (2009), 581–590. https://doi.org/10.1215/ijm/1266934794