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Laguerre Geometry of Surfaces in R 3
Acta Mathematica Sinica, English Series, 2005Let f : M → R3 be an oriented surface with non–degenerate second fundamental form. We denote by H and K its mean curvature and Gauss curvature. Then the Laguerre volume of f, defined by L(f) = f (H2 – K)/KdM, is an invariant under the Laguerre transformations. The critical surfaces of the functional L are called Laguerre minimal surfaces. In this paper
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Some Infinite Families of Locally Partial Geometries Generalizing the Classical Laguerre Planes
Starting with a subgeometry Ω embedded in a β-dimensional projective space PG(β, q), β ⩾ 1, we construct inductively a series of rank n residually connected geometries Γ(n, β, Ω), n ⩾ β, by putting Γ(β, β, Ω) = Ω and extending Γ(n - 1, β, Ω) with a ...
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