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

Year 2018, Volume: 1 Issue: 1, 23 - 26, 18.05.2018

Hakan Mete Taştan Sibel Gerdan

Abstract

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.

Keywords

Doubly Twisted Product Doubly Warped Product Semi-invariant Submanifold

References

  • 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.

Year 2018, Volume: 1 Issue: 1, 23 - 26, 18.05.2018

Hakan Mete Taştan Sibel Gerdan

Abstract

References

  • 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.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hakan Mete Taştan

Sibel Gerdan

Publication Date May 18, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

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. May 2018;1(1):23-26.
Chicago Taştan, Hakan Mete, and Sibel Gerdan. “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”. Mathematical Advances in Pure and Applied Sciences 1, no. 1 (May 2018): 23-26.
EndNote Taştan HM, Gerdan S (May 1, 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 and S. Gerdan, “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”, MAPAS, vol. 1, no. 1, pp. 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 (May 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 and Sibel Gerdan. “Doubly Twisted Product Semi-Invariant Submanifolds of a Locally Product Riemannian Manifold”. Mathematical Advances in Pure and Applied Sciences, vol. 1, no. 1, 2018, pp. 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.