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Generic warped product submanifolds in nearly Kaehler manifolds

Khan, V. A. and Khan, Khalid Ali (2009). Generic warped product submanifolds in nearly Kaehler manifolds. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry,50(2):337-352.

Document type: Journal Article
Citation counts: Scopus Citation Count Cited 5 times in Scopus Article | Citations
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Title Generic warped product submanifolds in nearly Kaehler manifolds
Author Khan, V. A.
Khan, Khalid Ali
Journal Name Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Publication Date 2009
Volume Number 50
Issue Number 2
ISSN 0138-4821   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-70450181543
Start Page 337
End Page 352
Total Pages 16
Place of Publication Germany
Publisher Springer
Field of Research MATHEMATICAL SCIENCES
Abstract Warped product manifolds provide excellent setting to model space-time near black holes or bodies with large gravitational force (cf. [1], [2], [14]). Recently, results are published exploring the existence (or non-existence) of warped product submanifolds in Kaehlerian and contact settings (cf. [6], [17], [20]). To continue the sequel, we have considered warped product submanifolds of nearly Kaehler manifolds with one of the factors a holomorphic submanifold. Such submanifolds are generic submanifolds in the sense of B. Y. Chen [5] and provide a generalization of CR and semi-slant submanifolds. It is shown that nearly Kaehler manifolds do not admit non-trivial warped product generic submanifolds, thereby generalizing the results of Chen [6] and Sahin [20]. However, non-trivial generic warped products (obtained by reversing the two factors of warped product generic submanifolds) exist in nearly Kaehler manifolds (cf. [21]). Some interesting results on the geometry of these submanifolds are obtained in the paper.
Keywords Generic warped products
Nearly Kaehler manifold
Semi-slant submanifold
Slant submanifold
Warped product
 
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Created: Fri, 29 Aug 2014, 17:44:57 CST by Anthony Hornby