Biharmonic pseudo-Riemannian submersions from 3-manifolds

Küpeli, İrem Erken; Murathan, Cengizhan

doi:10.2298/fil1802543e

Filomat

2018

DOI: 10.2298/fil1802543e

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Biharmonic pseudo-Riemannian submersions from 3-manifolds

İrem Erken Küpeli

Cengizhan Murathan

Abstract: We classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form onto a surface.

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2024

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References 13 publications

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Biharmonic curves along Riemannian submersions

Karakaş,

Şahin

2024

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The purpose of this paper is to study biharmonic curves along Riemannian submersions. We first consider a Riemannian submersion from a Riemannian manifold onto Riemannian manifold and investigate under what conditions a biharmonic curve on the total manifold is transformed to a biharmonic curve on the base manifold. We obtain several results with certain restrictions on curvatures. We then consider a Riemannian submersion from a Kaehler manifold onto a Riemannian manifold. Necessary and sufficient conditions were obtained for a curve that is biharmonic in the total manifold of Riemannian submersion to be biharmonic on the base manifold along the Riemannian submersion. In addition, considering the special cases of the curvatures of the curve, the biharmonicity of the curve on the base manifold is discussed.

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Biharmonic curves along Riemannian submersions

Karakaş,

Şahin

2024

MMN

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Biharmonic pseudo-Riemannian submersions from 3-manifolds

Abstract: We classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form onto a surface.

Cited by 1 publication

References 13 publications

Biharmonic curves along Riemannian submersions

Biharmonic curves along Riemannian submersions

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