IJPAM: Volume 116, No. 3 (2017)

Title

A SHORT NOTE ON RICCI TENSOR AND
BIHARMONIC HYPERSURFACES

Authors

Azam Etemad Dehkordy
Department of Mathematical Sciences
Isfahan University of Technology
Isfahan, IRAN

Abstract

There is a conjecture due to Chen, that every complete biharmonic submanifold of a Euclidean space is minimal. Several papers gave some affirmative partial answers to this conjecture. We focus on the spacial case in which the submanifold is a hypersurface in Euclidean space that its Ricci tensor satisfies special identity. We also obtain some results for $L_k$-biharmonic hypersurfaces with the same property.

History

Received: 2017-04-10
Revised: 2017-07-31
Published: October 25, 2017

AMS Classification, Key Words

AMS Subject Classification: 53C40, 53C42, 53C25
Key Words and Phrases: Ricci tensor, biharmonic hypersurface, $L_k$-biharmonic

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Bibliography

1
A. Balmus, S. Montaldo and C. Oniciuc, Biharmonic submanifolds in space forms, Symposium on the Differential Geometry of Submanifolds (2007), Valenciennes, France, 25-32.

2
B.Y. Chen, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), 169-188.

3
B. Y. Chen, Some open problems and conjectures on submanifolds of finite type: recent development, Tamkang J. Math. 45 (2014), 87-108, doi: https://doi.org/10.5556/j.tkjm.45.2014.1564.

4
B.Y. Chen, Some results on concircular vector fields and their applications to Riccisolitons, Bull. Korean Math. Soc. 52 (2015), 1535-1547, doi: https://doi.org/10.4134/BKMS.2015.52.5.1535.

5
I. Dimitric, Quadratic representation of a submanifold, Proc. Amer. Math. Soc, 114, No. 1 (1992), 201-210, doi: https://doi.org/10.2307/2159802.

6
A. Ferrandez and P. Lucas, Finite type hypersurfaces in space forms, Kodai Math. J., 14 (1991), 406-419, doi: https://doi.org/10.2996/kmj/1138039464.

7
M. Aminian and S.M.B. Kashani, $L_k$-biharmonic hypersurfaces in the Euclidian space, Taiwanese Journal of Mathematics, 19 (2015), 861-874, doi: https://doi.org/10.11650/tjm.18.2014.4830.

8
M. Mohammadpouri and S.M.B. Kashani, On some $L_k$-finite-type Euclidean hypersurfaces, International Scholarly Research Network ISRN Geometry, 1 (2012), Article ID 591296, 1-23, doi: https://doi.org/10.5402/2012/591296.

How to Cite?

DOI: 10.12732/ijpam.v116i3.5 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 3
Pages: 597 - 600


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