f -Biharmonic maps and f -biharmonic submanifolds II

Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of3-dimensional(κ,μ)-manifolds to be biharmonic.

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Onf-biharmonic maps andf-biharmonic submanifolds

Pacific Journal of Mathematics ◽

10.2140/pjm.2014.271.461 ◽

2014 ◽

Vol 271 (2) ◽

pp. 461-477 ◽

Cited By ~ 8

Author(s):

Ye-Lin Ou

Keyword(s):

Biharmonic Maps ◽

Biharmonic Submanifolds

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Biharmonic Maps from Tori into a 2-Sphere

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-018-0101-9 ◽

2018 ◽

Vol 39 (5) ◽

pp. 861-878

Author(s):

Zeping Wang ◽

Ye-Lin Ou ◽

Hanchun Yang

Keyword(s):

Biharmonic Maps

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Biharmonic submanifolds of Kaehler product manifolds

AIMS Mathematics ◽

10.3934/math.2021541 ◽

2021 ◽

Vol 6 (9) ◽

pp. 9309-9321

Author(s):

Yanlin Li ◽

◽

Mehraj Ahmad Lone ◽

Umair Ali Wani ◽

Keyword(s):

Biharmonic Submanifolds

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The index of biharmonic maps in spheres

Compositio Mathematica ◽

10.1112/s0010437x04001204 ◽

2005 ◽

Vol 141 (03) ◽

pp. 729-745 ◽

Cited By ~ 15

Author(s):

E. Loubeau ◽

C. Oniciuc

Keyword(s):

Biharmonic Maps

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Stability of Biharmonic Legendrian Submanifolds in Sasakian Space Forms

Canadian Mathematical Bulletin ◽

10.4153/cmb-2008-045-0 ◽

2008 ◽

Vol 51 (3) ◽

pp. 448-459 ◽

Cited By ~ 8

Author(s):

Toru Sasahara

Keyword(s):

Critical Points ◽

Harmonic Map ◽

Biharmonic Maps ◽

Space Forms ◽

Sasakian Space Forms ◽

The Stability ◽

Biharmonic Map ◽

Legendrian Submanifolds

AbstractBiharmonic maps are defined as critical points of the bienergy. Every harmonic map is a stable biharmonic map. In this article, the stability of nonharmonic biharmonic Legendrian submanifolds in Sasakian space forms is discussed.

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