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Volume 31 (2008)
- Issue 3 Pages 307-
- Issue 2 Pages 163-
- Issue 1 Pages 1-
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Volume 31, Issue 2
Displaying 1-7 of 7 articles from this issue
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Mutsuo Oka2008 Volume 31 Issue 2 Pages 163-182
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSPolar weighted homogeneous polynomials are special polynomials of real variables xi, yi, i = 1, ..., n with zi = xi + $¥sqrt{-1}$yi which enjoy a "polar action". In many aspects, their behavior looks like that of complex weighted homogeneous polynomials. We study basic properties of hypersurfaces which are defined by polar weighted homogeneous polynomials.View full abstractDownload PDF (190K) -
Georgi Ganchev, Velichka Milousheva2008 Volume 31 Issue 2 Pages 183-198
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSFor a two-dimensional surface M2 in the four-dimensional Euclidean space E4 we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and κ.
The condition k = κ = 0 characterizes the surfaces consisting of flat points. The minimal surfaces are characterized by the equality κ2 - k = 0. The class of the surfaces with flat normal connection is characterized by the condition κ = 0. For the surfaces of general type we obtain a geometrically determined orthonormal frame field at each point and derive Frenet-type derivative formulas.
We apply our theory to the class of the rotational surfaces in E4, which prove to be surfaces with flat normal connection, and describe the rotational surfaces with constant invariants.View full abstractDownload PDF (140K) -
Camille Plénat, Patrick Popescu-Pampu2008 Volume 31 Issue 2 Pages 199-218
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSLet (X,0) be a germ of complex analytic normal variety, non-singular outside 0. An essential divisor over (X,0) is a divisorial valuation of the field of meromorphic functions on (X,0), whose center on any resolution of the germ is an irreducible component of the exceptional locus. The Nash map associates to each irreducible component of the space of arcs through 0 on X the unique essential divisor intersected by the strict transform of the generic arc in the component. Nash proved its injectivity and asked if it was bijective. We prove that this is the case if there exists a divisorial resolution π of (X,0) such that its reduced exceptional divisor carries sufficiently many π-ample divisors (in a sense we define). Then we apply this criterion to construct an infinite number of families of 3-dimensional examples, which are not analytically isomorphic to germs of toric 3-folds (the only class of normal 3-fold germs with bijective Nash map known before).View full abstractDownload PDF (178K) -
Yoshiaki Fukuma2008 Volume 31 Issue 2 Pages 219-256
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSLet X be a projective variety of dimension n defined over the field of complex numbers and let L1, ..., Ln-i be ample line bundles on X, where i is an integer with 0 ≤ i ≤ n. In this paper, first, we define some invariants called the ith sectional H-arithmetic genus, the ith sectional geometric genus and the ith sectional arithmetic genus of (X, L1, ..., Ln-i). These are considered to be a generalization of invariants which have been defined in our previous papers. Moreover we investigate some basic properties of these, which are used in the second part and the third part of this work.View full abstractDownload PDF (270K) -
Takeshi Harui, Jiryo Komeda, Akira Ohbuchi2008 Volume 31 Issue 2 Pages 257-262
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSWe completely classify the pairs of two smooth plane curves with double coverings between them. More precisely, we show that there exist no double coverings between two smooth plane curves except for several special cases.View full abstractDownload PDF (73K) -
Masaya Maeda2008 Volume 31 Issue 2 Pages 263-271
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSDownload PDF (105K) -
Aurel Bejancu2008 Volume 31 Issue 2 Pages 272-306
Published: 2008
Released on J-STAGE: June 27, 2008
JOURNAL FREE ACCESSLet Fm = (M, F) be a Finsler manifold and G be the Sasaki-Finsler metric on TM°. We show that the curvature tensor field of the Levi-Civita connection on (TM°, G) is completely determined by the curvature tensor field of Vrănceanu connection and some adapted tensor fields on TM°. Then we prove that (TM°, G) is locally symmetric if and only if Fm is locally Euclidean. Also, we show that the flag curvature of the Finsler manifold Fm is determined by some sectional curvatures of the Riemannian manifold (TM°, G). Finally, for any c ≠ 0 we introduce the c-indicatrix bundle IM (c) and obtain new and simple characterizations of Fm of constant flag curvature c by means of geometric objects on both IM (c) and (TM°, G).View full abstractDownload PDF (232K)
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