KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2023 / Cilt: 16 Sayı: 1

Existence and Nonexistence of Warped Product Submanifolds of Almost Contact Manifolds

Abdulqader MUSTAFA
Cenap OZEL
Alexander PİGAZZİNİ
Richard PİNCAK
Sayfa
367–378
Yayın Tarihi
2023-04-30
DOI
—
🏛️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)

For further research direction, we addressed a couple of open problems arose from the results of this paper.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research.
📊
Temel Bulgular & Veri:Most of the results of this paper are general and decisive enough to generalize both known and new results.
💡
Sonuç & Katkı:For further research direction, we addressed a couple of open problems arose from the results of this paper.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Contact $CR$-warped products · Sasakian manifolds · Kenmotsu manifolds

Abstract

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both known and new results. Moreover, a discrete example of contact $CR$-warped product submanifold in Kenmotsu manifold is constructed. For further research direction, we addressed a couple of open problems arose from the results of this paper.

🔖

Bu Makaleye Atıf Yap

MUSTAFA, A., OZEL, C., PİGAZZİNİ, A., PİNCAK, R. (2023). Existence and Nonexistence of Warped Product Submanifolds of Almost Contact Manifolds. International Electronic Journal of Geometry, Cilt: 16 Sayı: 1, 367–378. https://ajindex.com/articles/929627

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (21)

  1. O’Neill, B.: Semi-Riemannian geometry with applictions to relativity, Academic Press, New York, 1983
  2. Bishop, R.L., O’Neill, B.: Manifolds of negative curvature, Transactions of the American Mathematical Society, 145, 1-49 (1969)
  3. Carmo, D.M.: Riemannian Geometry, Birkha¨user Boston, (1992)
  4. Bejancu, A.: Geometry of CR-submanifolds, D. Reidel Publishing Company, (1986)
  5. Chen, B.Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J., 41, 33-41 (1999)
  6. Chen, B.Y.: Geometry of slant submanifolds, Katholieke Universiteit Leuven, Leuven, (1990)
  7. Chen, B.Y.: On warped product immersions, Journal of Geometry, 82, 36-49 (2005)
  8. Chen, B.Y.: Geometry of warped products as Riemannian submanifolds and related problems, Soochow J. Math., 28, 125-156 (2002)
  9. Blair, D.E.: Almost contact manifolds with Killing structure tensors I. Pacific Journal of Mathematics, 39, 285-292 (1971)
  10. Oubina, J.A.: New classes of almost contact metric structures. Publicationes Mathematicae Debrecen, 32, 187-193 (1985)
  11. Sasaki, S.: On differentiable manifolds with certain structures which are closely related to almost contact structure. Tohoku Mathematical Journal, 12, 459-76 (1960)
  12. Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Mathematical Journal, 24, 93-103 (1972)
  13. Olszak, Z.: On almost cosymplectic manifolds. Kodai Mathematical Journal, 1, 239-250 (1981)
  14. Gray, A., Hervella, L.: The sixteen classes of almost Hermitian manifolds and their linear invariants. Annali di Matematica Pura ed Applicata, 123, 35-58 (1980)
  15. Gherghe, C.: Harmonicity of nearly trans-Sasaki manifolds. Demonstratio Mathematica, 33, 151-157 (2000)
  16. Chinea, D., Gonzalez, C.: A classification of almost contact metric manifolds, Annali di Matematica Pura ed Applicata, 156, 15-36 (1990)
  17. Marrero, J.C.: The local structure of trans-Sasakian manifolds. Annali di Matematica Pura ed Applicata, 162, 77-86 (1992)
  18. Khan, V.A., Khan, K.A., Uddin, S.: Contact CR-warped product submanifolds of Kenmotsu manifolds. Thai Journal of Mathematics, 6(1), 138-145 (2008)
  19. Munteanu, M.I.: Warped product contact CR-submanifolds of Sasakian space forms. Publicationes Mathematicae Debrecen, 66, 75-120 (2005)
  20. Chen, B.Y.: A survey on geometry of warped product submanifolds, J. Adv. Math. Stud. 6, 1-43 (2013)
  21. Mustafa, A., Uddin, S., Khan, V.A., Wong, B.R.: Contact