In particular, we prove that if a hypersurfaceis biharmonic, then it must have at least 6 distinct principal curvaturesunder the hypothesis of having mean curvature function satisfying thecondition above.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we study hypersurfaces with the mean curvature functionH satisfying $\langle \nabla H, \nabla H\rangle $ in a Minkowski space of arbitrary dimen-sion.
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Key Findings & Data:First, we obtain some conditions satised by connection forms ofbiconservative hypersurfaces with the mean curvature function whosegradient is light-like.
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Conclusion & Impact:In particular, we prove that if a hypersurfaceis biharmonic, then it must have at least 6 distinct principal curvaturesunder the hypothesis of having mean curvature function satisfying thecondition above.
In this paper we study hypersurfaces with the mean curvature functionH satisfying $\langle \nabla H, \nabla H\rangle $ in a Minkowski space of arbitrary dimen-sion. First, we obtain some conditions satised by connection forms ofbiconservative hypersurfaces with the mean curvature function whosegradient is light-like. Then, we use these results to get a classication ofbiharmonic hypersurfaces. In particular, we prove that if a hypersurfaceis biharmonic, then it must have at least 6 distinct principal curvaturesunder the hypothesis of having mean curvature function satisfying thecondition above.
Turgay, N. C. (2022). A classiffication of biharmonic hypersurfaces in the Minkowski spaces of arbitrary dimension. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 4, 1125–1134. https://ajindex.com/articles/530176