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f -Biharmonic Submanifolds in Space Forms and f -Biharmonic Riemannian Submersions from 3-Manifolds

Author

Listed:
  • Ze-Ping Wang

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

  • Li-Hua Qin

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

Abstract

f -biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of f -biharmonic curves in a space form. We also obtain a complete classification of proper f -biharmonic isometric immersions of a developable surface in R 3 by proving that a proper f -biharmonic developable surface exists only in the case where the surface is a cylinder. Based on this, we show that a proper biharmonic conformal immersion of a developable surface into R 3 exists only in the case when the surface is a cylinder. Riemannian submersions can be viewed as a dual notion of isometric immersions (i.e., submanifolds). We also study f -biharmonicity of Riemannian submersions from 3-manifolds by using the integrability data. Examples are given of proper f -biharmonic Riemannian submersions and f -biharmonic surfaces and curves.

Suggested Citation

  • Ze-Ping Wang & Li-Hua Qin, 2024. "f -Biharmonic Submanifolds in Space Forms and f -Biharmonic Riemannian Submersions from 3-Manifolds," Mathematics, MDPI, vol. 12(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1184-:d:1375997
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