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On the f-biharmonic Maps and Submanifolds

Mustapha Djaa|Kaddour Zegga|A. Mohamed cherif
경북대학교 자연과학대학 수학과|2015.03|Kyungpook Mathematical Journal|제55권 제1호|pp. 157-168|DOI http://dx.doi.org/10.5666/KMJ.2015.55.1.157

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참고문헌

키워드

Submanifoldsf-harmonic mapsf-biharmonic maps
주제분류수학

초록

In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into aRiemannian manifold with non-positive sectional curvature,satisfyingsome condition, is f-harmonic. Also we present some properties forthe f-biharmonicity of submanifolds of Sn, and wegive the classification of f-biharmonic curves in 3-dimensionalsphere.

Abstract

In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into aRiemannian manifold with non-positive sectional curvature,satisfyingsome condition, is f-harmonic. Also we present some properties forthe f-biharmonicity of submanifolds of Sn, and wegive the classification of f-biharmonic curves in 3-dimensionalsphere.

참고문헌 (12)

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  5. M. Djaa., "On The Generalized of Harmonic and Bi-harmonic Maps", International Electronic Journal of Geometry, 5(1), pp.90~100 (2012)
  6. J. Eells, "p-Harmonic and Exponentially Harmonic Maps", pp.1993
  7. J. Eells., "Harmonic mappings of Riemannian manifolds", Amer. J. Math, 86, pp.109~160 (1964)
  8. G. Y. Jiang, "2-Harmonic Maps Between Riemannian Manifolds", Annals of Math, China, 4, pp.389~402 (1986)
  9. E. Loubeau., "On the biharmonic and harmonic indices of the Hopf map", Transactions of the American Mathematical Society, 359, pp.5239~5256 (2007)
  10. S. Ouakkas, "R. Nasri and M. Djaa. On the f-harmonic and f-biharmonic maps", JP J. Geom. Topol, 10(1), pp.11~27 (2010)
  11. M. Rimoldi., "Topology of steady and expanding gradient solitons via f-harmonic maps", Diff. Geom. Appl, 31, pp.623~638 (2013)
  12. S. T. Yau, "Harmonic functions on complete Riemannian manifolds", Comm. Pure Appl. Math, 28, pp.201~228 (1975)

관련 논문AI추천

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