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$G_{3}$'te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri

Yıl 2021, Cilt: 23 Sayı: 2, 653 - 672, 04.07.2021

Bengü Bayram Özgün Biçgin

https://doi.org/10.25092/baunfbed.854728

Öz

n-boyutlu bağlantılı bir manifolddan m-boyutlu Öklid uzayına tanımlı bir izometrik daldırma için, M manifoldunun yer vektörü Laplas operatörünün sabit olmayan öz fonksiyonlarının sonlu bir toplamı olarak ayrışabiliyorsa, M manifoldu sonlu tiptedir, denir. Sonlu tipte yüzeyler farklı uzaylarda birçok yazar tarafından çalışılmıştır. Bu çalışmada, 3-boyutlu Galile uzayında, $\Delta ^{II}$ ikinci temel forma göre Laplas operatörü olmak üzere $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ eşitliğini sağlayan küresel çarpım yüzeylerini ele aldık. Ayrıca, bu yüzeylerin tam bir sınıflandırmasını verdik.

Anahtar Kelimeler

Sonlu tipte yüzeyler Galile uzayı küresel çarpım yüzeyi

Kaynakça

  • Arslan, K., Bulca, B., (Kilic) Bayram, B., Öztürk, G. and Ugail, H., On spherical product surfaces in , Institute of Electrical and Electronics Engineers Computer Society, Int. Conf. CYBERWORLDS, 132-137, (2009).
  • Aydın, M., E. and Öğrenmiş, A., O., Spherical Product Surface in The Galilean Space Konuralp Journal of Mathematics, 2, 290-298, (2016).
  • Aydın, M., E., Öğrenmiş A., O. and Ergüt, M., Classification Of Factorable Surfaces In The Psuedo Galilean Space, Glasnik Mathematicki, 70(50), 441-451, (2015).
  • Bekkar, M. and Senoussi, B., Factorable Surfaces In The Three-Dimensional Euclidean And Lorentzian Spaces Satisfying , Journal of Geometry, 103(1), 17-29, (2012).
  • Bekkar, M. and Senoussi, B., Translation Surfaces In The -Dimensional Space Satisfying , Journal of Geometry, 103, no. 3, 367-374, (2012).
  • Bulca, B., Arslan, K., (Kilic) Bayram, B., Öztürk, G., Spherical product surfaces in , Analele Stiintifice ale Universitatii Ovidius Constanta, 20, 41-54, (2012).
  • Chen, B., Y., Total Mean Curvature And Submanifolds of Finite Type, World Scientific, (1984).
  • Chen, B., Y., On The Total Curvature Of Immersed Manifolds, VI: Submanifolds of finite type and their application, Bulletin of the Institute of Mathematics Academia Sinica, 11, 309-328.
  • Çakmak, A., Karacan, M., K., Kiziltug, S. and Yoon, D., W., Translation Surfaces In The Three Dimensional Galilean Space Satisfying , Bulletin of the Korean Mathemathical Society, 54(4), 1241-1254, (2017).
  • Defever, F., Hypersurfaces Of With Harmonic Mean Curvature Vector Field, Mathematische Nachrichten, 196, 61-69, (1998).
  • Hasanis, Th., Vlachos, Th., Hypersurfaces In With Harmonic Mean Curvature Vector Field, Mathematische Nachrichten, 172, 145-169, (1995).
  • Jaclic, A., Leonordis, A. and Solina F., Segmentation And Recovery Of Superquadrics, Kluvar Academic Publishers, 20, (2000).
  • Kaimakamis, G., Papantoniou, B. and Petoumenos, K., Surfaces of Revolution In The 3- Dimensional Lorentz-Minkowski Space Satisfying , Bulletin of the Greek Mathematical Society, 50, 75-90, (2005).
  • Karacan, M., K., Yoon, D., W. and Bukcu, B., Translation Surfaces In The Three Dimensional Simply Isotropic Space , The International Journal of Geometric Methods in Modern Physics, 3, no. 7, 1650088, (2016).
  • Kisi, I., Öztürk, G., Spherical product surface having pointwise 1-type Gauss map in Galilean 3-space G₃, The International Journal of Geometric Methods in Modern Physics, 16, no. 12, 1950186, (2019).
  • Meng, H., and Liu, H., Factorable Surfaces In -Minkowski Space, Bulletin of the Korean Mathemathical Society, 46, no. 1, 155-169, (2009).
  • Senoussi, B. And Bekkar, M., Helicodial Surfaces With In The -Dimensional Euclidian Space, Studia Universitatis Babeș-Bolyai Mathematica, 60, no.3, 437-448, (2015).
  • Stamatakis, S. and Al-Zoubi, H., On Surface Of Finite Chen-Type, Results in Mathemathics, 43, no. 1-2, 181-190, (2003).
  • Takahashi, T., Minimal Immersions Of Riemannian Manifolds, The Journal of the Mathematical Society of Japan, 18, 380-385, (1966).
  • Yoon, D., W., Some Classification Of Translation Surfaces In Galilean -Space, International Journal of Mathematical Analysis, 6, no. 28, 1355-1361, (2012).
  • Yu, Y. and Liu, H., The Factorable Minimal Surfaces, Proceedings of The Eleventh International Workshop On Differential Geometry, 11, 33-39, (2007).
  • Biçgin, Ö., Galilean uzayda bazı yüzeylerin temel forma göre Laplasları, Yüksek Lisans Tezi, Balıkesir Üniversitesi, Fen Bilimleri Enstitüsü, Balıkesir, (2020).

Spherical product surfaces satisfying $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ in $\G_{3}$

Yıl 2021, Cilt: 23 Sayı: 2, 653 - 672, 04.07.2021

Bengü Bayram Özgün Biçgin

https://doi.org/10.25092/baunfbed.854728

Öz

For an isometric immersion of n-dimensional connected manifold into Euclidean m-space, the position vector of M can be decomposed as a finite sum of Em valued non-constant functions of the Laplacian operator, one can say that M is of finite type. Finite type surfacas corresponds to the fundamental forms are studied in different spaces by many authors. In this study, we consider the spherical product surface in 3-dimensional Galilean space satisfying the condition $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ where $\Delta ^{II}$ is the Laplacian with respect to second fundamental form. We also give exact classification of these type surfaces.

Anahtar Kelimeler

Finite type surface Galilean space spherical product surface

Kaynakça

  • Arslan, K., Bulca, B., (Kilic) Bayram, B., Öztürk, G. and Ugail, H., On spherical product surfaces in , Institute of Electrical and Electronics Engineers Computer Society, Int. Conf. CYBERWORLDS, 132-137, (2009).
  • Aydın, M., E. and Öğrenmiş, A., O., Spherical Product Surface in The Galilean Space Konuralp Journal of Mathematics, 2, 290-298, (2016).
  • Aydın, M., E., Öğrenmiş A., O. and Ergüt, M., Classification Of Factorable Surfaces In The Psuedo Galilean Space, Glasnik Mathematicki, 70(50), 441-451, (2015).
  • Bekkar, M. and Senoussi, B., Factorable Surfaces In The Three-Dimensional Euclidean And Lorentzian Spaces Satisfying , Journal of Geometry, 103(1), 17-29, (2012).
  • Bekkar, M. and Senoussi, B., Translation Surfaces In The -Dimensional Space Satisfying , Journal of Geometry, 103, no. 3, 367-374, (2012).
  • Bulca, B., Arslan, K., (Kilic) Bayram, B., Öztürk, G., Spherical product surfaces in , Analele Stiintifice ale Universitatii Ovidius Constanta, 20, 41-54, (2012).
  • Chen, B., Y., Total Mean Curvature And Submanifolds of Finite Type, World Scientific, (1984).
  • Chen, B., Y., On The Total Curvature Of Immersed Manifolds, VI: Submanifolds of finite type and their application, Bulletin of the Institute of Mathematics Academia Sinica, 11, 309-328.
  • Çakmak, A., Karacan, M., K., Kiziltug, S. and Yoon, D., W., Translation Surfaces In The Three Dimensional Galilean Space Satisfying , Bulletin of the Korean Mathemathical Society, 54(4), 1241-1254, (2017).
  • Defever, F., Hypersurfaces Of With Harmonic Mean Curvature Vector Field, Mathematische Nachrichten, 196, 61-69, (1998).
  • Hasanis, Th., Vlachos, Th., Hypersurfaces In With Harmonic Mean Curvature Vector Field, Mathematische Nachrichten, 172, 145-169, (1995).
  • Jaclic, A., Leonordis, A. and Solina F., Segmentation And Recovery Of Superquadrics, Kluvar Academic Publishers, 20, (2000).
  • Kaimakamis, G., Papantoniou, B. and Petoumenos, K., Surfaces of Revolution In The 3- Dimensional Lorentz-Minkowski Space Satisfying , Bulletin of the Greek Mathematical Society, 50, 75-90, (2005).
  • Karacan, M., K., Yoon, D., W. and Bukcu, B., Translation Surfaces In The Three Dimensional Simply Isotropic Space , The International Journal of Geometric Methods in Modern Physics, 3, no. 7, 1650088, (2016).
  • Kisi, I., Öztürk, G., Spherical product surface having pointwise 1-type Gauss map in Galilean 3-space G₃, The International Journal of Geometric Methods in Modern Physics, 16, no. 12, 1950186, (2019).
  • Meng, H., and Liu, H., Factorable Surfaces In -Minkowski Space, Bulletin of the Korean Mathemathical Society, 46, no. 1, 155-169, (2009).
  • Senoussi, B. And Bekkar, M., Helicodial Surfaces With In The -Dimensional Euclidian Space, Studia Universitatis Babeș-Bolyai Mathematica, 60, no.3, 437-448, (2015).
  • Stamatakis, S. and Al-Zoubi, H., On Surface Of Finite Chen-Type, Results in Mathemathics, 43, no. 1-2, 181-190, (2003).
  • Takahashi, T., Minimal Immersions Of Riemannian Manifolds, The Journal of the Mathematical Society of Japan, 18, 380-385, (1966).
  • Yoon, D., W., Some Classification Of Translation Surfaces In Galilean -Space, International Journal of Mathematical Analysis, 6, no. 28, 1355-1361, (2012).
  • Yu, Y. and Liu, H., The Factorable Minimal Surfaces, Proceedings of The Eleventh International Workshop On Differential Geometry, 11, 33-39, (2007).
  • Biçgin, Ö., Galilean uzayda bazı yüzeylerin temel forma göre Laplasları, Yüksek Lisans Tezi, Balıkesir Üniversitesi, Fen Bilimleri Enstitüsü, Balıkesir, (2020).
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Araştırma Makalesi
Yazarlar

Bengü Bayram 0000-0002-1237-5892

Özgün Biçgin 0000-0003-0255-8633

Yayımlanma Tarihi 4 Temmuz 2021
Gönderilme Tarihi 5 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 23 Sayı: 2

Kaynak Göster

APA Bayram, B., & Biçgin, Ö. (2021). $G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(2), 653-672. https://doi.org/10.25092/baunfbed.854728
AMA Bayram B, Biçgin Ö. $G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri. BAUN Fen. Bil. Enst. Dergisi. Temmuz 2021;23(2):653-672. doi:10.25092/baunfbed.854728
Chicago Bayram, Bengü, ve Özgün Biçgin. “$G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23, sy. 2 (Temmuz 2021): 653-72. https://doi.org/10.25092/baunfbed.854728.
EndNote Bayram B, Biçgin Ö (01 Temmuz 2021) $G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23 2 653–672.
IEEE B. Bayram ve Ö. Biçgin, “$G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri”, BAUN Fen. Bil. Enst. Dergisi, c. 23, sy. 2, ss. 653–672, 2021, doi: 10.25092/baunfbed.854728.
ISNAD Bayram, Bengü - Biçgin, Özgün. “$G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23/2 (Temmuz 2021), 653-672. https://doi.org/10.25092/baunfbed.854728.
JAMA Bayram B, Biçgin Ö. $G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri. BAUN Fen. Bil. Enst. Dergisi. 2021;23:653–672.
MLA Bayram, Bengü ve Özgün Biçgin. “$G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 23, sy. 2, 2021, ss. 653-72, doi:10.25092/baunfbed.854728.
Vancouver Bayram B, Biçgin Ö. $G_{3}$’te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri. BAUN Fen. Bil. Enst. Dergisi. 2021;23(2):653-72.