On minimality and scalar curvature of CMC triharmonic hypersurfaces in pseudo-Riemannian space forms (Q6594154)

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scientific article; zbMATH DE number 7902638
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On minimality and scalar curvature of CMC triharmonic hypersurfaces in pseudo-Riemannian space forms
scientific article; zbMATH DE number 7902638

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    On minimality and scalar curvature of CMC triharmonic hypersurfaces in pseudo-Riemannian space forms (English)
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    28 August 2024
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    The authors investigate the geometric properties of triharmonic hypersurfaces with constant mean curvature (CMC) in pseudo-Riemannian space forms, based on the assumption that the shape operator is diagonalizable.\N\NThe authors show that these triharmonic hypersurfaces must be minimal under a specific curvature multiplicity condition.\N\NAlso, the authors prove that a nonminimal triharmonic CMC hypersurface with diagonalizable shape operator in a non-flat pseudo-Riemannian space form has constant scalar curvature, and they provide a classification result for the cases \(c>0\) and \(c<0\).\N\NThis work provides an important contribution to differential geometry offering new insights into CMC triharmonic hypersurfaces.
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    pseudo-Riemannian space forms
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    triharmonic maps
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    hypersurfaces
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    constant mean curvature
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    diagonalizable shape operator
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