Kodai Mathematical Journal

Extrinsic homogeneous almost Hermitian 6-dimensional submanifolds in the octonions

Hideya Hashimoto, Takashi Koda, Katsuya Mashimo, Kouei Sekigawa

2007 年 30 巻 3 号 p. 297-321
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924936

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Helical geodesic immersions of semi-Riemannian manifolds

Kouhei Miura

2007 年 30 巻 3 号 p. 322-343
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924937

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We obtain some basic results on helical geodesic immersions in semi-Riemannian geometry. For example, it is shown that, for an indefinite semi-Riemannian submanifold, if any space-like geodesics of the submanifold are helices of order d, curvatures λ₁,...,λ_d-1 and signatures ε₁,...,ε_d in the ambient space, then any time-like geodesics of the submanifold have the same order and curvatures, and signatures (-1)¹ε₁,...,(-1)^dε_d.

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Simons-type inequalities for the compact submanifolds in the space of constant curvature

Jiancheng Liu, Qiuyan Zhang

2007 年 30 巻 3 号 p. 344-351
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924938

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For the compact submanifold M immersed in the standard Euclidean sphere S^n+p or the Euclidean space R^n+p, we obtain Simons-type inequalities about the first eigenvalue λ₁ and the squared norm of the second fundamental form S respectively. In particular, for the case of the ambient space is S^n+p, we need not the assumption that M is minimal. Following which, we obtain the estimate about the lower bound for S if it is constant respectively.

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On uniqueness of meromorphic functions in an angular domain

Zhao-Jun Wu

2007 年 30 巻 3 号 p. 352-360
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924939

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In this article, we investigate the uniqueness of meromorphic functions dealing with two shared values and a shared set in an angular domain. Results are obtained extending some results given by W. C. Lin and S. Mori.

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Semi-invariant lightlike submanifolds of a semi-Riemannian product manifold

Mehmet Atceken, Erol Kilic

2007 年 30 巻 3 号 p. 361-378
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924940

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In this paper, we introduce a new class of lightlike submanifolds, namely, semi-invariant lightlike submanifolds of a semi-Riemannian product manifold. We investigate totally umbilical, curvature invariant lightlike submanifolds in real space forms M₁(c₁) × M₂(c₂) and discuss integrabilities of distributions on semi-Riemannian product manifold.

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Non-hyperelliptic Riemann surfaces of genus five all of whose Weierstrass points have maximal weight

Ryutaro Horiuchi

2007 年 30 巻 3 号 p. 379-384
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924941

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It is proved that any non-hyperelliptic Riemann surface of genus five all of whose Weierstrass points have maximal weight has only Weierstrass points with gap sequence (1,2,3,5,9), and a defining equation of such a surface is given.

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Domains of variability of Laurent coefficients and the convex hull for the family of concave univalent functions

Bappaditya Bhowmik, Saminathan Ponnusamy, Karl-Joachim Wirths

2007 年 30 巻 3 号 p. 385-393
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924942

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Let D denote the open unit disc and let p ∈ (0,1). We consider the family Co(p) of functions f : D → $¥overline{{¥mathbf C}}$ that satisfy the following conditions:
(i) f is meromorphic in D and has a simple pole at the point p.
(ii) f(0) = f′(0) – 1 = 0.
(iii) f maps D conformally onto a set whose complement with respect to $¥overline{{¥mathbf C}}$ is convex.
We determine the exact domains of variability of some coefficients a_n (f) of the Laurent expansion
f (z) = $¥sum_{n=-1}^{¥infty}$ a_n (f)(z − p)ⁿ, |z − p| < 1 − p,
for f ∈ Co(p) and certain values of p. Knowledge on these Laurent coefficients is used to disprove a conjecture of the third author on the closed convex hull of Co(p) for certain values of p.

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Analytic computation of some automorphism groups of Riemann surfaces

James S. Wolper

2007 年 30 巻 3 号 p. 394-408
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924943

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Equations for the locus of Riemann Surfaces of genus three with a nonabelian automorphism group generated by involutions are determined from vanishings of Riemann's theta function.

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On sequentially Cohen-Macaulay modules

Nguyen Tu Cuong, Doan Trung Cuong

2007 年 30 巻 3 号 p. 409-428
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924944

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In this paper we introduce the notion of good systems of parameters with respect to certain increasing filtration of submodules of a Noetherian module in order to prove several characterizations of sequentially Cohen-Macaulay modules in terms of good systems of parameters. The sequential Cohen-Macaulayness of Stanley-Reisner rings of small embedding dimension are also examined.

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Regular separation with parameter of complex analytic sets

Maciej P. Denkowski

2007 年 30 巻 3 号 p. 429-437
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924945

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The aim of this paper is to prove that a pair of analytic sets X, Y ⊂ C_z^m × C_wⁿ is locally regularly separated with a uniform exponent α in the fibres taken over a proper projection π(z,w) = z of X ∩ Y (under the assumption that X ∩ Y has pure dimension): for all z ∈ π (X ∩ Y) ∩ U, dist(w,Y^z) ≥ const.dist(w,(X ∩ Y)^z)^α when w ∈ X^z ∩ V, where U × V is a neighbourhood of a point a ∈ X ∩ Y such that π(a) is regular in π(X ∩ Y). As an application of this we obtain a parameter version of the Łojasiewicz inequality for c-holomorphic mappings. Both results are a complex counterpart of the main result of [ŁW] from the subanalytic case, extended in this paper by a bound on the uniform exponent.

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Some generalizations of Nevanlinna's five-value theorem

Ten-Ging Chen, Keng-Yan Chen, Yen-Lung Tsai

2007 年 30 巻 3 号 p. 438-444
発行日: 2007年
公開日: 2007/11/02

DOIhttps://doi.org/10.2996/kmj/1193924946

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We generalize Nevanlinna's five-value theorem to the cases that two meromorphic functions partially sharing either five or more values, or five or more small functions. In each case, we formulate a way to measure how far these two meromorphic functions are from sharing either values or small functions, and use this measurement to get some uniqueness results.

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