منابع مشابه
Hyperbolic surfaces of $L_1$-2-type
In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.
متن کاملThe Geometry of Rank 2 Hyperbolic Root Systems
Let ∆ be a rank 2 hyperbolic root system. Then ∆ has generalized Cartan matrix H(a, b) = ( 2 −b −a 2 ) indexed by a, b ∈ Z with ab ≥ 5. If a 6= b, then ∆ is non-symmetric and is generated by one long simple root and one short simple root, whereas if a = b, ∆ is symmetric and is generated by two long simple roots. We prove that if a 6= b, then ∆ contains an infinite family of symmetric rank 2 hy...
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We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of PG(3, q), for q congruent to -1 modulo 12, 24, 60 respectively, from the root systems of type D4, F4, H4, respectively. The smallest member of each of these families is an exceptional flock. We then characterise these partial flocks in terms of the rectangle condition of Benz and by not be...
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Let f : X → X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We show that in the class of C, r > 0, cocycles with fiber special Euclidean group SE(n) those that are transitive form a residual set (countable intersection of open dense sets). This result is new for n ≥ 3 odd. More generally, we consider Euclidean-type groups GnR where G is a compact connected Lie group a...
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A geometric charactrization of the equation found by Hietarinta and Viallet, which satisfies the singularity confinement criterion but which exhibits chaotic behavior, is presented. It is shown that this equation can be lifted to an automorphism of a certain rational surface and can therefore be considered to be a realization of a Cremona isometry on the Picard group of the surface. It is also ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1979
ISSN: 0001-8708
DOI: 10.1016/s0001-8708(79)80003-1