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- W3194420148 abstract "In this paper we deal with non-degenerate surfaces $Sigma^2$ immersed in the $3$-dimensional homogeneous space $mathbb{L}^{3}(kappa,tau)$ endowed with two different metrics, the one induced by the Riemannian metric of $mathbb{E}^3(kappa,tau)$ and the non-degenerate metric inherited by the Lorentzian one of $mathbb{L}^3(kappa,tau)$. Therefore, we have two different geometries on $Sigma^2$ and we can compare them. In particular, we study the case where the mean curvature functions with respect to both metrics simultaneously vanish, and in this case we show that the surface is ruled. Furthermore, we consider the case where both mean curvature functions coincide but do not necessarily vanish and we also consider the situation where the extrinsic curvatures with respect to both metrics coincide." @default.
- W3194420148 created "2021-08-30" @default.
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- W3194420148 date "2021-08-15" @default.
- W3194420148 modified "2023-09-27" @default.
- W3194420148 title "On the geometry of non-degenerate surfaces in Lorentzian homogeneous $3$-manifolds" @default.
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