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Volume 64 (2012)
- Issue 4 Pages 1053-
- Issue 3 Pages 683-
- Issue 2 Pages 343-
- Issue 1 Pages 1-
Predecessor
- Proceedings of the Physico-Mathematical Society of Japan. 3rd Series
- Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series
- Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo
- Tokyo Sugaku-Butsurigakkwai Hokoku
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku Kaisya Zasshi
Volume 64, Issue 3
Displaying 1-13 of 13 articles from this issue
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Gopal Prasad, Sai-Kee Yeung2012 Volume 64 Issue 3 Pages 683-731
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSThe quotient of a Hermitian symmetric space of non-compact type by a torsion-free cocompact arithmetic subgroup of the identity component of the group of isometries of the symmetric space is called an arithmetic fake compact Hermitian symmetric space if it has the same Betti numbers as the compact dual of the Hermitian symmetric space. This is a natural generalization of the notion of “fake projective planes” to higher dimensions. Study of arithmetic fake compact Hermitian symmetric spaces of type An with even n has been completed in [PY1], [PY2]. The results of this paper, combined with those of [PY2], imply that there does not exist any arithmetic fake compact Hermitian symmetric space of type other than An, n ≤ 4 (see Theorems 1 and 2 in the Introduction below and Theorem 2 of [PY2]). The proof involves the volume formula given in [P], the Bruhat-Tits theory of reductive p-adic groups, and delicate estimates of various number theoretic invariants.View full abstractDownload PDF (401K) -
Shun Shimomura2012 Volume 64 Issue 3 Pages 733-781
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSThe discrete second Painlevé equation dPII is mapped to the second Painlevé equation PII by its continuous limit, and then, as shown by Kajiwara et al., a rational solution of dPII also reduces to that of PII. In this paper, regarding dPII as a difference equation, we present a certain asymptotic solution that reduces to a triply-truncated solution of PII in this continuous limit. In a special case our solution corresponds to a rational one of dPII. Furthermore we show the existence of families of solutions having sequential limits to truncated solutions of PII.View full abstractDownload PDF (345K) -
Tomohiro Kawakami, Kota Takeuchi, Hiroshi Tanaka, Akito Tsuboi2012 Volume 64 Issue 3 Pages 783-797
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSIn this paper we study (strongly) locally o-minimal structures. We first give a characterization of the strong local o-minimality. We also investigate locally o-minimal expansions of (R, +, <).View full abstractDownload PDF (231K) -
Yu Kawakami, Daisuke Nakajo2012 Volume 64 Issue 3 Pages 799-821
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSWe give the best possible upper bound for the number of exceptional values of the Lagrangian Gauss map of complete improper affine fronts in the affine three-space. We also obtain the sharp estimate for weakly complete case. As an application of this result, we provide a new and simple proof of the parametric affine Bernstein problem for improper affine spheres. Moreover, we get the same estimate for the ratio of canonical forms of weakly complete flat fronts in hyperbolic three-space.View full abstractDownload PDF (269K) -
Kouki Taniyama2012 Volume 64 Issue 3 Pages 823-849
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSWe define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. We define and study several multiplicities in the category of topological spaces and continuous maps, the category of groups and homomorphisms, the category of finitely generated R-modules and R-linear maps over a principal ideal domain R, and the neighbourhood category of oriented knots in the 3-sphere.View full abstractDownload PDF (320K) -
Mitsuhiro Nakao2012 Volume 64 Issue 3 Pages 851-883
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSWe derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u|αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.View full abstractDownload PDF (267K) -
The Anh Bui2012 Volume 64 Issue 3 Pages 885-902
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSLet L be a non-negative self adjoint operator on L2(X) where X is a space of homogeneous type. Assume that L generates an analytic semigroup e-tL whose kernel satisfies the standard Gaussian upper bounds. By the spectral theory, we can define the spectral multiplier operator F(L). In this article, we show that the commutator of a BMO function with F(L) is bounded on Lp(X) for 1 < p < ∞ when F is a suitable function.View full abstractDownload PDF (236K) -
Alexander Arhangel′skii, Jan van Mill2012 Volume 64 Issue 3 Pages 903-926
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSIt is shown that all uniquely homogeneous spaces are connected. We characterize the uniquely homogeneous spaces that are semitopological or quasitopological groups. We identify two properties of homogeneous spaces called skew-2-flexibility and 2-flexibility that are useful in studying unique homogeneity. We also construct a large family of uniquely homogeneous spaces with only trivial continuous maps.View full abstractDownload PDF (259K) -
Francesco Guaraldo2012 Volume 64 Issue 3 Pages 927-939
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSSome basic results on compact affine Nash groups related to their Nash representations are given. So, first a Nash version of the Peter-Weil theorem is proved and then several more results are given: for example, it is proved that an analytic representation of such a group is of class Nash and that the category of the classes of isomorphic embedded compact Nash groups is isomorphic with that of the classes of isomorphic embedded algebraic groups. Moreover, given a compact affine Nash group G, a closed subgroup H and a homogeneous Nash G-manifold X, it is proved that the twisted product G ×H X is a Nash G-manifold which is Nash G-diffeomorphic to an algebraic G-variety; besides, this algebraic structure is unique.View full abstractDownload PDF (193K) -
Gianluca Occhetta, Valentina Paterno2012 Volume 64 Issue 3 Pages 941-967
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSIn this paper we study smooth complex projective polarized varieties (X,H) of dimension n ≥ 2 which admit a covering family V of rational curves of degree 3 with respect to H such that two general points of X may be joined by a curve parametrized by V, and such that there is a covering family of rational curves of H-degree one.
We prove that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjunction theoretic scroll structure over a smooth variety.View full abstractDownload PDF (302K) -
Toshiaki Adachi2012 Volume 64 Issue 3 Pages 969-984
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSWe study the global behavior of trajectories for Kähler magnetic fields on a connected complete Kähler manifold M of negative curvature. Concerning these trajectories we show that theorems of Hadamard-Cartan type and of Hopf-Rinow type hold: If sectional curvatures of M are not greater than c (< 0) and the strength of a Kähler magnetic field is not greater than $¥sqrt{|c|}$, then every magnetic exponential map is a covering map. Hence arbitrary distinct points on M can be joined by a minimizing trajectory for this magnetic field.View full abstractDownload PDF (213K) -
Rafael López, Marian Ioan Munteanu2012 Volume 64 Issue 3 Pages 985-1003
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSIn the homogeneous space Sol3, a translation surface is parametrized by x(s,t) = α(s) * β(t), where α and β are curves contained in coordinate planes and * denotes the group operation of Sol3. In this paper we study translation surfaces in Sol3 whose mean curvature vanishes.View full abstractDownload PDF (205K) -
Ryushi Goto2012 Volume 64 Issue 3 Pages 1005-1052
Published: 2012
Released on J-STAGE: September 07, 2012
JOURNAL FREE ACCESSLet X0 be an affine variety with only normal isolated singularity at p. We assume that the complement X0 \ {p} is biholomorphic to the cone C(S) of an Einstein-Sasakian manifold S of real dimension 2n − 1. If there is a resolution of singularity π: X → X0 with trivial canonical line bundle KX, then there is a Ricci-flat complete Kähler metric for every Kähler class of X. We also obtain a uniqueness theorem of Ricci-flat conical Kähler metrics in each Kähler class with a certain boundary condition. We show there are many examples of Ricci-flat complete Kähler manifolds arising as crepant resolutions.View full abstractDownload PDF (372K)
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