Journal of Mahani Mathematical Research

Journal of Mahani Mathematical Research

Proper biharmonic $G$-invariant hypersurfaces in Minkowski 4-space

Document Type : Research Paper

Authors
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran
Abstract
In this paper, we study properly biharmonic hypersurfaces in the Minkowski 4-space $\mathbb{E}_1^4$ that are invariant under the action of some Lie groups of isometries. Using the symmetries imposed by Lie groups, we provide a complete local classification of such hypersurfaces according to the causal character of the orbits and the ambient pseudouclidean metric. Explicit parametrizations are obtained for all non-degenerate cases, and geometric properties such as the mean curvature, shape operator, and biconservative condition are analyzed in detail. Several examples are presented to illustrate the theory. Our results generalize previous classifications of biconservative hypersurfaces in Euclidean and Lorentzian settings and highlight the interplay between group symmetry and higher-order geometric constraints.
Keywords
Subjects

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Articles in Press, Accepted Manuscript
Available Online from 02 July 2026

  • Receive Date 19 January 2026
  • Revise Date 06 June 2026
  • Accept Date 29 June 2026