KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Existence of Warped Product Submanifolds of Almost Hermitian Manifolds

Abdulqader MUSTAFA
Cenap ÖZEL
Sayfa
361–370
Yayın Tarihi
2022-10-18
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 Hermitian manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of other researchers, which is the second goal.
📊
Temel Bulgular & Veri:At the end of the paper a list of warped products is tabulated whether exist or not.
💡
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:CR-warped products · Kaehler · nearly Kaehler

Abstract

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost Hermitian manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of other researchers, which is the second goal. At the end of the paper a list of warped products is tabulated whether exist or not. Moreover, a discrete example of $CR$-warped product submanifold in Kaehler 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., ÖZEL, C. (2022). Existence of Warped Product Submanifolds of Almost Hermitian Manifolds. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 361–370. https://ajindex.com/articles/539573

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. Bejancu, A.: CR submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69, 135-142 (1978)
  2. Bejancu, A.: Geometry of CR-submanifolds. D. Reidel Publishing Company (1986)
  3. Bishop, R. L., O’Neill, B.: Manifolds of negative curvature, Transactions of the American Mathematical Society. 145, 1-49 (1969)
  4. Chen, B. Y.: Geometry of slant submanifolds. Katholieke Universiteit Leuven, Leuven (1990)
  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 warped product CR-submanifolds in Kaehler manifolds. Monatshefte für Mathematik, 133, 177-195 (2001)
  7. Chen, B. Y.:Geometry of warped products as Riemannian submanifolds and related problems, Soochow J. Math. 28, 125-156 (2002)
  8. Chen, B. Y.: On warped product immersions, Journal of Geometry, 82 (1-2), 36-40 (2005)
  9. Chen, B. Y.: A survey on geometry of warped product submanifolds, J. Adv. Math. Stud. 6, (2), 1-43 (2013)
  10. Do Carmo, M.: Riemannian Geometry. Birkhauser. Boston (1992)
  11. Khan, V. A. & Khan, K. A.: Generic warped product submanifolds in nearly Kaehler manifolds. Contributions to Algebra and Geometry. 50(2), 337-352 (2009)
  12. Moroianu, A.: Lectures on Kaehler Geometry, Cambridge University Press (2007)
  13. Mustafa, A., De, A. and Uddin, S.: Characterization of warped product submanifolds in Kenmotsu manifolds, Balkan J. Geom. Appl. 20 (1), 86-97 (2015)
  14. Nash, J. F.: C1-isometric imbeddings, Annals Math. 60(3), 383-396 (1954)
  15. Nash, J. F.: The imbedding problem for Riemannian manifolds, Annals Math. 63(1), 20-63 (1956)
  16. O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. New York (1983)
  17. Sahin, B.: Non-existence of warped product semi-slant submanifolds of Kaehler manifolds. Geometriae Dedicata,117,195-202 (2006).