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The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 283–298 | Cite as

Biconservative Submanifolds in \(\mathbb {S}^n\times \mathbb {R}\) and \(\mathbb {H}^n\times \mathbb {R}\)

  • F. Manfio
  • N. C. Turgay
  • A. UpadhyayEmail author
Article
  • 132 Downloads

Abstract

In this paper we study biconservative submanifolds in \(\mathbb {S}^n\times \mathbb {R}\) and \(\mathbb {H}^n\times \mathbb {R}\) with parallel mean curvature vector field and codimesion 2. We obtain some sufficient and necessary conditions for such submanifolds to be conservative. In particular, we obtain a complete classification of 3-dimensional biconservative submanifolds in \(\mathbb {S}^4\times \mathbb {R}\) and \(\mathbb {H}^4\times \mathbb {R}\) with nonzero parallel mean curvature vector field. We also get some results for biharmonic submanifolds in \(\mathbb {S}^n\times \mathbb {R}\) and \(\mathbb {H}^n\times \mathbb {R}\).

Keywords

Biconservative submanifolds Biharmonic submanifolds Product spaces \(\mathbb {S}^n\times \mathbb {R}\) and \(\mathbb {H}^n\times \mathbb {R}\) 

Mathematics Subject Classification

Primary 53A10 Secondary 53C40, 53C42 

Notes

Acknowledgements

The third author gratefully thanks for the support from the National Post-doctoral Fellowship of Science and Engineering Research Board (SERB), Government of India.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Universidade de São PauloSão CarlosBrazil
  2. 2.Department of Mathematics, Faculty of Science and LettersIstanbul Technical UniversityMaslakTurkey
  3. 3.Department of MathematicsIndian Institute of ScienceBengaluruIndia

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