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- Title
Hypersurfaces with parallel Laguerre form in ℝ<sup>n</sup>.
- Authors
Shichang Shu
- Abstract
For a given (n - 1)-dimensional hypersurface x : M → ℝn, 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.
- Subjects
LAGUERRE geometry; HYPERSURFACES; IMMERSIONS (Mathematics); EIGENVALUES; TENSOR algebra
- Publication
Balkan Journal of Geometry & Its Applications, 2017, Vol 22, Issue 2, p75
- ISSN
1224-2780
- Publication type
Article