<i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds
<i>f</i>-biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of <i>f</i>-biharmonic curves in a space form. We also obtain a complete classification of proper <i>f</i>-biharmonic isometric immersions o...
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MDPI AG
2024-04-01
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| author | Ze-Ping Wang Li-Hua Qin |
| author_facet | Ze-Ping Wang Li-Hua Qin |
| author_sort | Ze-Ping Wang |
| collection | DOAJ |
| description | <i>f</i>-biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of <i>f</i>-biharmonic curves in a space form. We also obtain a complete classification of proper <i>f</i>-biharmonic isometric immersions of a developable surface in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula> by proving that a proper <i>f</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula> 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 <i>f</i>-biharmonicity of Riemannian submersions from 3-manifolds by using the integrability data. Examples are given of proper <i>f</i>-biharmonic Riemannian submersions and <i>f</i>-biharmonic surfaces and curves. |
| first_indexed | 2025-03-22T05:56:33Z |
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| language | English |
| last_indexed | 2025-03-22T05:56:33Z |
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| spelling | doaj.art-525c4f2bc0dc4d64a6fb8dcd5ddedf7f2024-04-26T13:34:57ZengMDPI AGMathematics2227-73902024-04-01128118410.3390/math12081184<i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-ManifoldsZe-Ping Wang0Li-Hua Qin1School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaSchool of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China<i>f</i>-biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of <i>f</i>-biharmonic curves in a space form. We also obtain a complete classification of proper <i>f</i>-biharmonic isometric immersions of a developable surface in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula> by proving that a proper <i>f</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula> 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 <i>f</i>-biharmonicity of Riemannian submersions from 3-manifolds by using the integrability data. Examples are given of proper <i>f</i>-biharmonic Riemannian submersions and <i>f</i>-biharmonic surfaces and curves.https://www.mdpi.com/2227-7390/12/8/1184biharmonic maps<i>f</i>-biharmonic mapsRiemannian submersions<i>f</i>-biharmonic curves<i>f</i>-biharmonic submanifolds |
| spellingShingle | Ze-Ping Wang Li-Hua Qin <i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds Mathematics biharmonic maps <i>f</i>-biharmonic maps Riemannian submersions <i>f</i>-biharmonic curves <i>f</i>-biharmonic submanifolds |
| title | <i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds |
| title_full | <i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds |
| title_fullStr | <i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds |
| title_full_unstemmed | <i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds |
| title_short | <i>f</i>-Biharmonic Submanifolds in Space Forms and <i>f</i>-Biharmonic Riemannian Submersions from 3-Manifolds |
| title_sort | i f i biharmonic submanifolds in space forms and i f i biharmonic riemannian submersions from 3 manifolds |
| topic | biharmonic maps <i>f</i>-biharmonic maps Riemannian submersions <i>f</i>-biharmonic curves <i>f</i>-biharmonic submanifolds |
| url | https://www.mdpi.com/2227-7390/12/8/1184 |
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