Biconservative Lorentz hypersurfaces in $\mathbb{E}_{1}^{\lowercase{n}+1}$ with complex eigenvalues

Ram Shankar Gupta; A. Sharfuddin

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arXiv · 1706.00783

Biconservative Lorentz hypersurfaces in $\mathbb{E}_{1}^{\lowercase{n}+1}$ with complex eigenvalues

Ram Shankar Gupta·A. Sharfuddin

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Abstract

Our paper is an attempt to to verify the Chen's conjecture on biharmonic submanifolds and to classify biconservative submanifolds. In doing so we provide an affirmative answer to Chen's conjecture on biharmonic submanifolds. We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in $\mathbb{E}_{1}^{n+1}$ having complex eigenvalues has constant mean curvature. Moreover, every biharmonic Lorentz hypersurface $M_{1}^{n}$ having complex eigenvalues in $\mathbb{E}_{1}^{n+1}$ must be minimal.

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BibTeX RIS

Ram Shankar Gupta, A. Sharfuddin. 2017-06-02. Biconservative Lorentz hypersurfaces in $\mathbb{E}_{1}^{\lowercase{n}+1}$ with complex eigenvalues. https://arxiv.org/abs/1706.00783

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