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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

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

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 Articles
Yazarlar

Hakan Mete Taştan

Sibel Gerdan

Yayımlanma Tarihi 18 Mayıs 2018
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.
AMA Taştan HM, Gerdan S. Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. MAPAS. Mayıs 2018;1(1):23-26.
Chicago 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 1, sy. 1 (Mayıs 2018): 23-26.
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 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, 2018.
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 (Mayıs 2018), 23-26.
JAMA 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, 2018, ss. 23-26.
Vancouver Taştan HM, Gerdan S. Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold. MAPAS. 2018;1(1):23-6.