All issues
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 1
Displaying 1-14 of 14 articles from this issue
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Toshiaki Adachi2012 Volume 64 Issue 1 Pages 1-21
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSWe study lengths of helices of orders 3 and 4 which are generated by some Killing vector fields on a complex projective plane and on a complex hyperbolic plane. We consider the moduli space of such helices under the congruence relation and give a lamination structure on this space which are closely related with the length spectrum. This shows that the moduli space does not form a canonical building structure with respect to the length spectrum.View full abstractDownload PDF (263K) -
Toshikazu Takagi2012 Volume 64 Issue 1 Pages 23-85
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSLet p be a prime not equal to 2 or 3. We determine the group of all modular units on the modular curve X1(2p), and its full cuspidal class number. We mention a fact concerning the non-existence of torsion points of order 5 or 7 of elliptic curves over Q of square-free conductor n as an application of a result by Agashe and the cuspidal class number formula for X0(n). We also state the formula for the order of the subgroup of the Q-rational torsion subgroup of J1(2p) generated by the Q-rational cuspidal divisors of degree 0.View full abstractDownload PDF (451K) -
Toshikazu Takagi2012 Volume 64 Issue 1 Pages 87-89
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSWe correct a theorem on the conductor of elliptic curves over Q given in Introduction of the paper “The cuspidal class number formula for the modular curves X1(2p)”.View full abstractDownload PDF (112K) -
Toshio Sumi2012 Volume 64 Issue 1 Pages 91-106
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSFor a finite group G, an $¥mathscr{L}$(G)-free gap G-module V is a finite dimensional real G-representation space satisfying the two conditions: (1) VL = 0 for any normal subgroup L of G with prime power index. (2) dim VP > 2 dim VH for any P < H ≤ G such that P is of prime power order. A finite group G not of prime power order is called a gap group if there is an $¥mathscr{L}$(G)-free gap G-module. We give a necessary and sufficient condition for that G is a gap group for a finite group G satisfying that G/[G,G] is not a 2-group, where [G,G] is the commutator subgroup of G.View full abstractDownload PDF (232K) -
Vladimir S. Matveev2012 Volume 64 Issue 1 Pages 107-152
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSWe describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces, prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces, and prove the two-dimensional pseudo-Riemannian version of the projective Obata conjecture.View full abstractDownload PDF (600K) -
Roberto Monti, Daniele Morbidelli2012 Volume 64 Issue 1 Pages 153-179
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSGiven a strictly pseudoconvex hypersurface M ⊂ Cn+1, we discuss the problem of classifying all local CR diffeomorphisms between open subsets N, N′ ⊂ M. Our method exploits the Tanaka-Webster pseudohermitian invariants of a contact form ϑ on M, their transformation formulae, and the Chern-Moser invariants. Our main application concerns a class of generalized ellipsoids where we classify all local CR mappings.View full abstractDownload PDF (284K) -
The necessary and sufficient condition for the group of leaf preserving diffeomorphisms to be simpleKazuhiko Fukui2012 Volume 64 Issue 1 Pages 181-184
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSLet $¥mathscr{F}$ be a C∞-foliation on a compact C∞-manifold M. We consider the group of all leaf preserving C∞-diffeomorphisms of (M, $¥mathscr{F}$) which are isotopic to the identity through leaf preserving C∞-diffeomorphisms. Then we show that the group is simple if and only if all leaves of $¥mathscr{F}$ are dense.View full abstractDownload PDF (134K) -
Kei Kondo, Minoru Tanaka2012 Volume 64 Issue 1 Pages 185-200
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSThis article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold M. In the first series [KT1], we showed that all Busemann functions on an M which is not less curved than a von Mangoldt surface of revolution $¥widetilde{M}$ are exhaustions, if the total curvature of $¥widetilde{M}$ is greater than π. A von Mangoldt surface of revolution is, by definition, a complete surface of revolution homeomorphic to R2 whose Gaussian curvature is non-increasing along each meridian. Our purpose of this series is to generalize the main theorem in [KT1] to an M which is not less curved than a more general surface of revolution.View full abstractDownload PDF (216K) -
Mitsuru Nakai2012 Volume 64 Issue 1 Pages 201-229
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSIt is shown that there exists a Riemann surface on which every Dirichlet finite harmonic function is automatically bounded and yet the linear dimension of the linear space of Dirichlet finite harmonic functions on it is infinite.View full abstractDownload PDF (265K) -
Shigeru Mukai2012 Volume 64 Issue 1 Pages 231-246
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSA (holomorphic) involution σ of an Enriques surface S is said to be numerically reflective if it acts on the cohomology group H2(S, Q) as a reflection. We show that the invariant sublattice H(S, σ; Z) of the anti-Enriques lattice H-(S, Z) under the action of σ is isomorphic to either ⟨-4⟩ ⊥ U(2) ⊥ U(2) or ⟨-4⟩ ⊥ U(2) ⊥ U. Moreover, when H(S, σ; Z) is isomorphic to ⟨-4⟩ ⊥ U(2) ⊥ U(2), we describe (S, σ) geometrically in terms of a curve of genus two and a Göpel subgroup of its Jacobian.View full abstractDownload PDF (245K) -
Peter Hästö, Henri Lindén, Ana Portilla, José ...2012 Volume 64 Issue 1 Pages 247-261
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSWe derive explicit and simple conditions which in many cases allow one to decide, whether or not a Denjoy domain endowed with the Poincaré or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows us to deduce the non-hyperbolicity of any periodic Denjoy domain.View full abstractDownload PDF (235K) -
Mohammad Alakhrass2012 Volume 64 Issue 1 Pages 263-272
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSLet Ω be a Brelot space satisfying the domination principle and has a positive potential. We define the superharmonic extension property (SEP) for Ω and introduce a sufficient condition under which Ω has the SEP property. We give a characterization of the extreme Jensen measures in a Brelot space with SEP property.View full abstractDownload PDF (175K) -
Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai2012 Volume 64 Issue 1 Pages 273-316
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSDifferential operators on Siegel modular forms which behave well under the restriction of the domain are essentially intertwining operators of the tensor product of holomorphic discrete series to its irreducible components. These are characterized by polynomials in the tensor of pluriharmonic polynomials with some invariance properties. We give a concrete study of such polynomials in the case of the restriction from Siegel upper half space of degree 2n to the product of degree n. These generalize the Gegenbauer polynomials which appear for n = 1. We also describe their radial parts parametrization and differential equations which they satisfy, and show that these differential equations give holonomic systems of rank 2n.View full abstractDownload PDF (359K) -
Humio Ichimura, Shoichi Nakajima2012 Volume 64 Issue 1 Pages 317-342
Published: 2012
Released on J-STAGE: February 24, 2012
JOURNAL FREE ACCESSLet p be an odd prime number and ℓ a prime number with ℓ ≠ p. Let Kn = Q(ζpn+1) be the pn+1-st cyclotomic field. Let hn and hn- be the class number and the relative class number of Kn, respectively. When ℓ = 2, we give an explicit bound mp depending on p such that the ratio hn-/hn-1- is odd for all n > mp. When ℓ ≥ 3, we also give a corresponding result on the ℓ-part of the relative class number of Kn+(ζℓ). As an application, we show that when p ≤ 509, the ratio hn/h0 is odd for all n ≥ 1.View full abstractDownload PDF (307K)
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