Hypersurfaces with parallel Laguerre form in R

نویسنده

  • Shichang Shu
چکیده

For a given (n − 1)-dimensional hypersurface x : M → R, consider the Laguerre form Φ, the Laguerre tensor L and the Laguerre second fundamental form B of the immersion x. In this article, we address the case when the Laguerre form of x is parallel, i.e., ∇Φ ≡ 0. We prove that ∇Φ ≡ 0 is equivalent to Φ ≡ 0, provided that either L+λB+μg = 0 for some smooth function λ and μ, or x has constant Laguerre eigenvalues, or x has constant para-Laguerre eigenvalues, where ∇ is the Levi-Civita connection of the Laguerre metric g. M.S.C. 2010: 53A40, 53B25.

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تاریخ انتشار 2017