- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 724898, 12 pages
Warped Product Submanifolds of Riemannian Product Manifolds
1Department of Mathematics, King Abdulaziz University, P.O. Box 80015, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia
Received 11 June 2012; Accepted 21 September 2012
Academic Editor: Xiaodong Yan
Copyright © 2012 Falleh R. Al-Solamy and Meraj Ali Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. L. Bishop and B. O'Neill, “Manifolds of negative curvature,” Transactions of the American Mathematical Society, vol. 145, pp. 1–49, 1969.
- S.-T. Hong, “Warped products and black holes,” Il Nuovo Cimento della Società Italiana di Fisisca B, vol. 120, no. 10-11, pp. 1227–1234, 2005.
- B.-Y. Chen, “Geometry of warped product CR-submanifolds in Kaehler manifolds,” Monatshefte für Mathematik, vol. 133, no. 3, pp. 177–195, 2001.
- M. Atçeken, “Warped product semi-slant submanifolds in locally Riemannian product manifolds,” Bulletin of the Australian Mathematical Society, vol. 77, no. 2, pp. 177–186, 2008.
- X. Senlin and N. Yilong, “Submanifolds of product Riemannian manifold,” Acta Mathematica Scientia Series B, vol. 20, no. 2, pp. 213–218, 2000.
- M. Atçeken, “Slant submanifolds of a Riemannian product manifold,” Acta Mathematica Scientia Series B, vol. 30, no. 1, pp. 215–224, 2010.
- N. Papaghiuc, “Semi-slant submanifolds of a Kaehlerian manifold,” Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi, vol. 40, no. 1, pp. 55–61, 1994.
- J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Semi-slant submanifolds of a Sasakian manifold,” Geometriae Dedicata, vol. 78, no. 2, pp. 183–199, 1999.
- A. Carriazo, New Developments in Slant Submanifolds Theory, Narosa Publishing House, New Delhi, India, 2002.
- V. A. Khan and M. A. Khan, “Pseudo-slant submanifolds of a Sasakian manifold,” Indian Journal of Pure and Applied Mathematics, vol. 38, no. 1, pp. 31–42, 2007.
- B. Sahin, “Warped product submanifolds of Kaehler manifolds with a slant factor,” Annales Polonici Mathematici, vol. 95, no. 3, pp. 207–226, 2009.
- S. Hiepko, “Eine innere Kennzeichnung der verzerrten Produkte,” Mathematische Annalen, vol. 241, no. 3, pp. 209–215, 1979.