[1] Han Yingbo,. Biharmonic product mapsbetween doubly warped product manifolds [J]. Journal of Southeast University (English Edition), 2010, 26 (3): 502-504. [doi:10.3969/j.issn.1003-7985.2010.03.027]

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Biharmonic product mapsbetween doubly warped product manifolds()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

26

Issue:

2010 3

Page:

502-504

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2010-09-30

Info

Title:

Biharmonic product mapsbetween doubly warped product manifolds

Author(s):

Han Yingbo

Department of Mathematics, Southeast University, Nanjing 211189, China
College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China

Keywords:

biharmonic map;  product map;  doubly warped product manifolds

PACS:

O186.1

DOI:

10.3969/j.issn.1003-7985.2010.03.027

Abstract:

The biharmonicity of the product map Φ_2=φ×ψ2 and the two generalized projections (-overφ) and (-overψ) are analyzed. Some results are obtained, that is, Φ₂ is a proper biharmonic map if and only if b is a non-constant solution of -1/(f ^2)J_φ2(dφ(grad(lnb)))+(n)/2grad|dφ(grad(lnb))|²=0 and f is a non-constant solution of -1/(b^2)J_ψ2(dψ(grad(lnf)))+(m)/2grad|dψ(grad(lnf))|²=0, and Φ₂=φ×ψ is a proper biharmonic map if and only if (-overφ) and (-overψ) are proper biharmonic maps.

References:

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[2] Jiang G Y. 2-harmonic maps and their first and second variation formulas [J]. Chi Ann Math Ser A, 1986, 7(4):389-402.
[3] Eells J, Sampson J H. Harmonic maps of Riemannian manifolds [J]. Amer J Math, 1964, 86(1):109-160.
[4] Loubeau E, Oniciuc C. The index of biharmonic maps in spheres [J]. Compos Math, 2005, 141(3):729-745.
[5] Oniciuc C. On the second variation formula for biharmonic maps to a sphere [J]. Publ Math Debrecen, 2002, 61(3):613-622.
[6] Balmus A, Monaldo S, Oniciuc C. Biharmonic maps between warped product manifolds [J]. J Geom Phys, 2007, 57(2):449-466.
[7] Bishop R L, O’Neil B. Manifolds of negative curvature [J]. Amer Math Soc, 1969, 145(1):1-49.
[8] Perktas S Y, Kilic E. Biharmonic maps doubly warped product manifolds [J]. Balk J of Geom and Its Appli, 2010, 15(2):151-162.

Memo

Memo:

Biography: Han Yingbo(1978—), male, doctor, yingbhan@yahoo.com.cn.
Foundation item: The National Natural Science Foundation of China(No.10971029).
Citation: Han Yingbo.Biharmonic product maps between doubly warped product manifolds[J].Journal of Southeast University(English Edition), 2010, 26(3):502-504.

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