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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

Some Results of $f$-Harmonic and Bi-$f$-Harmonic Maps with Potential

Zegga KADDOUR
Pages
157–166
Publication Date
2021-04-15
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

More, we study the case of conformal maps between equidimensional manifolds.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this note, we characterize the $f$-harmonic maps and bi-$f$-harmonic maps with potential.
📊
Key Findings & Data:We prove that every bi-$f$-harmonic map with potential from complete Riemannian manifold, satisfying some conditions is a $f$-harmonic map with potential.
💡
Conclusion & Impact:More, we study the case of conformal maps between equidimensional manifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:f-harmonic maps with potential · bi-f-harmonic maps with potential · H-f-energy

Abstract

In this note, we characterize the $f$-harmonic maps and bi-$f$-harmonic maps with potential. We prove that every bi-$f$-harmonic map with potential from complete Riemannian manifold, satisfying some conditions is a $f$-harmonic map with potential. More, we study the case of conformal maps between equidimensional manifolds.

Özet

In this note we characterize the f-harmonic maps and bi-f-harmonic maps with potential.We prove that every bi-f-harmonic map with potential from complete Riemannian manifold, satisfying some conditions is a f-harmonic map with potential.

🔖

Cite This Article

KADDOUR, Z. (2021). Some Results of $f$-Harmonic and Bi-$f$-Harmonic Maps with Potential. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 157–166. https://ajindex.com/articles/672066

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References (14)

  1. Lichnerowicz, A.: Applications harmoniques et variétés Kähleriennes. Rend. Sem. Mat. Fis. Milano. 39, 186–195 (1969)
  2. Cherif, A. M., Djaa, M.: On the bi-harmonic maps with potential. Arab J. Math. Sci. 24(1), 1–8 (2018)
  3. Ratto, A.: Harmonic maps with potential. Proceedings of theWorkshop on Differential Geometry and Topology (Palermo, 1996). Rend. Circ. Mat. Palermo. (2) Suppl. No. 49, 229–242 (1997)
  4. Zagane, A., Ouakass, S.: Some results and examples of the biharmonic maps with potential. Arab J. Math. Sci. 24(2), 182–198 (2018)
  5. Zegga, K., Cherif, A. M., Djaa, M.: On the f-biharmonic maps and submanifolds. Kyungpook Math. J. 55(1), 157–168 (2015)
  6. Ara, M. Geometry of F-harmonic maps. Kodai Math. J. 22(2), 243–263 (1999)
  7. Djaa, M., Cherif, A. M., Zegga, K., Ouakkas, S.: On the generalized of harmonic and bi-harmonic maps. Int. Electron. J. Geom. 5(1), 90–100 (2012)
  8. Cherif, A. M., Djaa, M., Zegga, K.: Stable f-harmonic maps on sphere. Commun. Korean Math. Soc. 30(4), 471–479 (2015)
  9. Course N.: f-harmonic maps, Thesis, University ofWarwick, Coventry, CV4 7AL, UK,2004
  10. Baird, P.: Harmonic maps with symmetry, harmonic morphisms and deformations of metrics. Research Notes in Mathematics, 87. Pitman (Advanced Publishing Program), Boston, MA, 1983
  11. Chen, Q.: Harmonic maps with potential from complete manifolds. Chinese Sci. Bull. 43(21), 1780–1786 (1998)
  12. Jiang, R.: Harmonic maps with potential from R2 into S2. Asian J. Math. 20(4), 597–627 (2016)
  13. Ouakkas, S., Nasri, R., Djaa, M.: On the f-harmonic and f-biharmonic maps. JP J. Geom. Topol. 10(1), 11–27 (2010)
  14. Branding, V.: The heat flow for the full bosonic string. Ann. Global Anal. Geom. 50(4), 347–365 (2016).