Research Article
BibTex RIS Cite

Helis Hiperyüzeyleri Tarafından Elde Edilen Konvolüsyon Manifoldların Karakterizasyonları Üzerine

Year 2020, Volume: 10 Issue: 3, 631 - 640, 15.07.2020
https://doi.org/10.17714/gumusfenbil.617238

Abstract

Bu
çalışmada, düzlemsel eğrilerden elde edilen iki helis hiperyüzey
immersiyonlarının tensör çarpımları tarafından elde edilen bir altmanifold
oluşturuldu. Bu altmanifoldun, konvolüsyon metrik ile birlikte bir konvolüsyon manifold
olduğu görüldü ve bu manifoldun minimalliği incelendi. Daha sonra aynı
altmanifoldun tamamen geodezikliğine bakılarak bazı karakterizasyonlar verildi.

References

  • Aksoy, A., 2008. Tensör Çarpım İmmersiyonlarının Geometrisi. Phd Thesis. İnönü Üniversitesi Fen Bilimleri Enstitüsü, Malatya, 107s.
  • Arslan, K., Ezentas, R., Mihai, I., Murathan, C. and Özgür, C., 2001.Tensor Product Surfaces of a Euclidean Space Curve and a Euclidean Plane Curve, Beitra ̈ge zur Algebra und Geometrie. 42 (2), 523-530.
  • Barrera Cadena, C., J. Di Scala, A., Ruiz-Hernández, G., 2015. Helix Surfaces in Euclidean Spaces. Beitra ̈ge zur Algebra und Geometrie, 56, 551–573.
  • Chen, B.Y., 1973. Geometry of Submanifolds, M. Dekker, New York, 298p.
  • Chen, B.Y., 2002. Convolution of Riemannian Manifolds and its Applications. Bulletin of the Australian Mathematical Society, 66(2), 177-191.
  • Chen, B.Y., 2003. More on Convolution of Riemannian Manifolds. Contributions to Algebra and Geometry, 44(1), 9-24.
  • Decruyenaere, F., Dillen, F., Verstraelen, L. and Vrancken, L., 1993. The Semiring of Immersions of Manifolds. Beiträge Algebra Geometrie (Contrib. Alg. Geom.), 34, 209-215.
  • Di Scala, AJ., Ruiz-Hernández, G., 2009. Helix Submanifolds of Euclidean Spaces. Monatshefte für Mathematik 157, 205–215.
  • Di Scala, AJ., Ruiz- Hernández, G., 2010. Higher Codimensional Euclidean Helix Submanifolds. Kodai Mathematical Journal. 33(2), 192-210.
  • Di Scala, AJ., Ruiz-Hernández, G., 2016. Minimal Helix Submanifolds and Minimal Riemannian Foliations. Boletín de la Sociedad Matemática Mexicana, 22, 229–250.
  • Fetcu, D., 2015. A Classification Result for Helix Surfaces with Parallel Mean Curvature in Product Spaces. Arkiv för Matematik, 53, 249–258.
  • Kula, L., Ekmekci, N., Yaylı, Y., İlarslan, K., 2010. Characterizations of Slant Helices in Euclidean 3-Space. Turkish Journal of Mathematics, 34, 261–273.
  • Küçükarslan, Y.Z., Yıldırım, Y.M., 2018. On k-Type 2-Degenerate Slant Helices in 4-Dimensional Minkowski Space-Time. Journal of Advanced Physics, 7(1), 147-151.
  • Mihai, I., Rosca, R., Verstraelen, L., Vrancken, L., 1994/1995. Tensor Product Surfaces of Euclidean Planar Curves. Rendiconti del Seminario Matematico di Messina, 3, 181-188.
  • O'neill, B., 1983.Semi-Riemannian Geometry, Academic Press, New York, 483p.
  • Zıplar, E., 2012. Helix Hypersurfaces and Special Curves. International Journal of Contemporary Mathematical Sciences, 7( 25), 1233–1245.

On the Characterizations of Convolution Manifolds Obtained by Helix Hypersurfaces

Year 2020, Volume: 10 Issue: 3, 631 - 640, 15.07.2020
https://doi.org/10.17714/gumusfenbil.617238

Abstract


In this study, a submanifold obtained by tensor product of the immersions of two helix hypersurfaces obtained by planar curves is constructed. It is seen that, this submanifold is a convolution manifold with convolution metric and  its minimality is examined. After, some characterizations are given by looking at the totally geodesic of same submanifold.

References

  • Aksoy, A., 2008. Tensör Çarpım İmmersiyonlarının Geometrisi. Phd Thesis. İnönü Üniversitesi Fen Bilimleri Enstitüsü, Malatya, 107s.
  • Arslan, K., Ezentas, R., Mihai, I., Murathan, C. and Özgür, C., 2001.Tensor Product Surfaces of a Euclidean Space Curve and a Euclidean Plane Curve, Beitra ̈ge zur Algebra und Geometrie. 42 (2), 523-530.
  • Barrera Cadena, C., J. Di Scala, A., Ruiz-Hernández, G., 2015. Helix Surfaces in Euclidean Spaces. Beitra ̈ge zur Algebra und Geometrie, 56, 551–573.
  • Chen, B.Y., 1973. Geometry of Submanifolds, M. Dekker, New York, 298p.
  • Chen, B.Y., 2002. Convolution of Riemannian Manifolds and its Applications. Bulletin of the Australian Mathematical Society, 66(2), 177-191.
  • Chen, B.Y., 2003. More on Convolution of Riemannian Manifolds. Contributions to Algebra and Geometry, 44(1), 9-24.
  • Decruyenaere, F., Dillen, F., Verstraelen, L. and Vrancken, L., 1993. The Semiring of Immersions of Manifolds. Beiträge Algebra Geometrie (Contrib. Alg. Geom.), 34, 209-215.
  • Di Scala, AJ., Ruiz-Hernández, G., 2009. Helix Submanifolds of Euclidean Spaces. Monatshefte für Mathematik 157, 205–215.
  • Di Scala, AJ., Ruiz- Hernández, G., 2010. Higher Codimensional Euclidean Helix Submanifolds. Kodai Mathematical Journal. 33(2), 192-210.
  • Di Scala, AJ., Ruiz-Hernández, G., 2016. Minimal Helix Submanifolds and Minimal Riemannian Foliations. Boletín de la Sociedad Matemática Mexicana, 22, 229–250.
  • Fetcu, D., 2015. A Classification Result for Helix Surfaces with Parallel Mean Curvature in Product Spaces. Arkiv för Matematik, 53, 249–258.
  • Kula, L., Ekmekci, N., Yaylı, Y., İlarslan, K., 2010. Characterizations of Slant Helices in Euclidean 3-Space. Turkish Journal of Mathematics, 34, 261–273.
  • Küçükarslan, Y.Z., Yıldırım, Y.M., 2018. On k-Type 2-Degenerate Slant Helices in 4-Dimensional Minkowski Space-Time. Journal of Advanced Physics, 7(1), 147-151.
  • Mihai, I., Rosca, R., Verstraelen, L., Vrancken, L., 1994/1995. Tensor Product Surfaces of Euclidean Planar Curves. Rendiconti del Seminario Matematico di Messina, 3, 181-188.
  • O'neill, B., 1983.Semi-Riemannian Geometry, Academic Press, New York, 483p.
  • Zıplar, E., 2012. Helix Hypersurfaces and Special Curves. International Journal of Contemporary Mathematical Sciences, 7( 25), 1233–1245.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sema Kazan 0000-0002-8771-9506

Publication Date July 15, 2020
Submission Date September 9, 2019
Acceptance Date May 13, 2020
Published in Issue Year 2020 Volume: 10 Issue: 3

Cite

APA Kazan, S. (2020). Helis Hiperyüzeyleri Tarafından Elde Edilen Konvolüsyon Manifoldların Karakterizasyonları Üzerine. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(3), 631-640. https://doi.org/10.17714/gumusfenbil.617238