Complex hyperbolic space and compact quotients
COMMUTING ISOMETRIES OF THE COMPLEX HYPERBOLIC SPACE
... Let g be elliptic. It follows from the conjugacy classification that all the eigen- values have norm 1, and it has a negative eigenvalue. If the negative eigenvalue has multiplicity at least 2, then it is called a ...
Application of an integral formula to CR submanifolds of complex hyperbolic space
... OF COMPLEX HYPERBOLIC SPACE JIN SUK PAK AND HYANG SOOK KIM Received 24 May 2004 and in revised form 2 March 2005 The purpose of this paper is to study n-dimensional compact CR-submanifolds of ...
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Compact hyperbolic coxeter thin cubes
... of hyperbolic coxeter ...no compact hyperbolic coxeter polytopes in H n when n ≥ 30 ...the hyperbolic coxeter pyramids in terms of coxeter diagram and John Mcleod generalized it in his article ...
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Complex hyperbolic triangle groups
... Therefore at least one of θ, φ or θ + φ is an integer multiple of 2π and hence A has an eigenvalue 1. Thus the remaining two eigenvalues are conjugate and we have trace A = 1 + 2 cos θ. Assume that w A is elliptic of ...
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CiteSeerX — On The Eigenmodes Of Compact Hyperbolic 3-Manifolds
... Having established that our algorithm is reliable, we set it loose on the SnapPea census to produce the list of lowest eigenvalues recorded in Table 4. The lowest eigenvalue, q 21 , is a useful topological invariant that ...
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Compact Minimal CR Submanifolds of a Complex Projective Space with Positive Ricci Curvature
... 3. Integral formula In this section, for later use, we compute the Laplacian for the square of the length of the second fundamental form A of an n-dimensional minimal submanifold M immersed in a complex projective ...
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Horo-tight circles in hyperbolic space
... In this section we prepare some notations and definitions which we will use for the proof of the main theorem. A Morse function ϕ on a manifold M is called a perfect function if 1. M r (ϕ) = {x ∈ M | ϕ(x) 6 r} is ...
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Hypersurfaces in Hyperbolic Space with Support Function
... develop the global correspondence between admissible hypersurfaces H n+1 and realizable metrics on domains in S n . We also prove that an admissible hypersurface can be unfolded into an embedded one along the normal flow ...
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Traces in Complex Hyperbolic Triangle Groups
... The space of such groups of fixed signature is of real dimension ...this space by a real invariant α of triangles in the complex hy- perbolic ...
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Clustering and the hyperbolic geometry of complex networks
... is hyperbolic. One of the basic features of a hyperbolic space is that the volume growth is exponential which is also the case, for example, when one considers a k-ary tree, that is, a rooted tree ...
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Clustering and the hyperbolic geometry of complex networks
... There is no particular reason why a random geometric graph on a Euclidean space would be intrinsically associated with the formation of a complex network. Real-world networks consist of heterogeneous nodes, ...
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Tilings to Nets: a Journey through Hyperbolic Space
... Illustrations of the maximum tilings are found in figure 0.3. The group ∗ 642 /OOO consists, as one would expect, of a quotient of a group ∗ 642 by a normal subgroup OOO thereof. The tilings that these groups correspond ...
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Space-only hyperbolic approximation of the Vlasov equation
... The Particle-In-Cell (PIC) method (see for instance [3,14]) is a popular method for computing collisionless plasma, because it allows performing simulations in complex configurations with a relatively low amount ...
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Harmonic Analysis on Quantum Complex Hyperbolic Spaces
... Consider the group SU n,m and its homogeneous space H n,m = SU n,m /S(U n,m−1 × U 1 ). The latter is called a complex hyperbolic space. The Faraut paper [5] on such pseudo-Hermitian symmetric ...
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Complex hyperbolic geometry of the figure-eight knot
... V C D fZ 2 C 2 ;1 j hZ; Zi > 0g; V 0 D fZ 2 C 2 ;1 f0g j hZ; Zi D 0g; V D fZ 2 C 2 ;1 j hZ; Zi < 0g: Let P W C 2 ;1 nf0g ! P C 2 be the canonical projection onto complex projective space, and let PU ...
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Compact difference scheme for two dimensional fourth order hyperbolic equation
... fourth-order hyperbolic equation ...the compact operators to ap- proximate the second-order derivatives in the space variables and rewrite the above prob- lem as an initial value problem for a system ...
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Complete noncompact CMC surfaces in hyperbolic 3 space
... the boundary values of R 1 and R 2 to obtain compact error terms. We now briefly describe the appropriate operator spaces and basic results that we will need to make the above sketch argument more precise. We ...
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HYPERBOLIC SPACE GROUPS FOUR SERIES WITH SIMPLICIAL DOMAINS
... Introduction Hyperbolic space groups are isometric groups, acting discontinuously on the hyperbolic 3-space with compact fundamental ...a space group by Poincare Theorem [1], ...
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Hyperbolic metrics on universal Teichmüller space and extremal problems
... to complex geometry of the universal Teichm¨ uller ...this space coincide and apply this impor- tant fact to solving the general extremal problems for univalent functions with quasiconformal ...
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Mixed foliate CR submanifolds in a complex hyperbolic space are non proper
... For simplicity, we assume that H m is the (complex) m-dimensional complex hyperbolic space with constant holomorphic sectional curvature -4. We denote by < ) the metric tensor of H m [r] ...
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