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Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold

Yıl 2018, Cilt: 1 Sayı: 1, 23 - 26, 18.05.2018

Hakan Mete Taştan , Sibel Gerdan

https://izlik.org/JA44DH49JM

Öz

We define the notion of nearly doubly twisted product of type 1 and 2. We
prove that there do not exist doubly twisted (respectively, doubly warped) product
semi-invariant submanifolds in locally product Riemannian manifolds other than
nearly doubly twisted product of type 2 (respectively, warped product) semi-invariant
submanifolds.

Anahtar Kelimeler

Doubly Twisted Product Doubly Warped Product Semi-invariant Submanifold

Kaynakça

  • A. Bejancu, \textit{Semi-invariant submanifolds of locally product Riemannian manifolds}, An. Univ. Timisoara, \textbf{22} (1984).
  • R.L. Bishop and B. O'neill, \textit{Manifolds of negative curvature}, Trans, Amer. Math. Soc.,\textbf{145} (1969), 1-49.
  • B.Y. Chen, \emph{Differential geometry of warped product manifolds and submanifolds}, World Scientific, 2017.
  • B.Y.Chen, \textit{Geometry of warped product CR-submanifolds in Kaehler manifold}, Monatsh. Math., \textbf{133} (2001), 177-195.
  • B.Y. Chen, \emph{Differential geometry of warped product manifolds and submanifolds}, World Scientific, 2017. B.Y. Chen, \emph{Geometry of submanifolds and its applications}, Science University of Tokyo, 1981.
  • M. Fernandez Lopez, E. Garcia-Rio, D. N. Kupeli, B. Ünal, \textit{A curvature condition for a twisted product to be a warped product}, Manuscripta Math., \textbf{106} (2001), 213-217.
  • M.I. Muntenau, \textit{Doubly warped product CR-submanifolds in locally conformal K\"{a}hler manifolds}, Monatsh. Math. , \textbf{150} (2007), 333-342.
  • B. \d{S}ahin, \textit{Notes on doubly warped and doubly twisted product CR-submanifolds of Kaehler manifolds}, Mat. Vesnik \textbf{59} (2007), 205-210. B. \d{S}ahin and M. At\c{c}eken, \textit{Semi-invariant submanifolds of Riemannian product manifold}, BJGA, \textbf{8}, No:1 (2003), 91-100.
  • S. Uddin, \textit{On doubly warped and doubly twisted product submanifolds}, Int. Elect. J. Geo. \textbf{3}, No:1 (2010), 35-39.
  • Yano, K. and Kon, M. \emph{Structures on manifolds}, World Scientific, Singapore, 1984.

Yıl 2018, Cilt: 1 Sayı: 1, 23 - 26, 18.05.2018

Hakan Mete Taştan , Sibel Gerdan

https://izlik.org/JA44DH49JM

Öz

Kaynakça

  • A. Bejancu, \textit{Semi-invariant submanifolds of locally product Riemannian manifolds}, An. Univ. Timisoara, \textbf{22} (1984).
  • R.L. Bishop and B. O'neill, \textit{Manifolds of negative curvature}, Trans, Amer. Math. Soc.,\textbf{145} (1969), 1-49.
  • B.Y. Chen, \emph{Differential geometry of warped product manifolds and submanifolds}, World Scientific, 2017.
  • B.Y.Chen, \textit{Geometry of warped product CR-submanifolds in Kaehler manifold}, Monatsh. Math., \textbf{133} (2001), 177-195.
  • B.Y. Chen, \emph{Differential geometry of warped product manifolds and submanifolds}, World Scientific, 2017. B.Y. Chen, \emph{Geometry of submanifolds and its applications}, Science University of Tokyo, 1981.
  • M. Fernandez Lopez, E. Garcia-Rio, D. N. Kupeli, B. Ünal, \textit{A curvature condition for a twisted product to be a warped product}, Manuscripta Math., \textbf{106} (2001), 213-217.
  • M.I. Muntenau, \textit{Doubly warped product CR-submanifolds in locally conformal K\"{a}hler manifolds}, Monatsh. Math. , \textbf{150} (2007), 333-342.
  • B. \d{S}ahin, \textit{Notes on doubly warped and doubly twisted product CR-submanifolds of Kaehler manifolds}, Mat. Vesnik \textbf{59} (2007), 205-210. B. \d{S}ahin and M. At\c{c}eken, \textit{Semi-invariant submanifolds of Riemannian product manifold}, BJGA, \textbf{8}, No:1 (2003), 91-100.
  • S. Uddin, \textit{On doubly warped and doubly twisted product submanifolds}, Int. Elect. J. Geo. \textbf{3}, No:1 (2010), 35-39.
  • Yano, K. and Kon, M. \emph{Structures on manifolds}, World Scientific, Singapore, 1984.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Hakan Mete Taştan

Sibel Gerdan

Yayımlanma Tarihi 18 Mayıs 2018
IZ https://izlik.org/JA44DH49JM
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 1

Kaynak Göster

APA Taştan, H. M., & Gerdan, S. (2018). Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. Mathematical Advances in Pure and Applied Sciences, 1(1), 23-26. https://izlik.org/JA44DH49JM
AMA 1.Taştan HM, Gerdan S. Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. MAPAS. 2018;1(1):23-26. https://izlik.org/JA44DH49JM
Chicago Taştan, Hakan Mete, ve Sibel Gerdan. 2018. “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”. Mathematical Advances in Pure and Applied Sciences 1 (1): 23-26. https://izlik.org/JA44DH49JM.
EndNote Taştan HM, Gerdan S (01 Mayıs 2018) Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. Mathematical Advances in Pure and Applied Sciences 1 1 23–26.
IEEE [1]H. M. Taştan ve S. Gerdan, “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”, MAPAS, c. 1, sy 1, ss. 23–26, May. 2018, [çevrimiçi]. Erişim adresi: https://izlik.org/JA44DH49JM
ISNAD Taştan, Hakan Mete - Gerdan, Sibel. “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”. Mathematical Advances in Pure and Applied Sciences 1/1 (01 Mayıs 2018): 23-26. https://izlik.org/JA44DH49JM.
JAMA 1.Taştan HM, Gerdan S. Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. MAPAS. 2018;1:23–26.
MLA Taştan, Hakan Mete, ve Sibel Gerdan. “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”. Mathematical Advances in Pure and Applied Sciences, c. 1, sy 1, Mayıs 2018, ss. 23-26, https://izlik.org/JA44DH49JM.
Vancouver 1.Taştan HM, Gerdan S. Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. MAPAS [Internet]. 01 Mayıs 2018;1(1):23-6. Erişim adresi: https://izlik.org/JA44DH49JM