巻号一覧
52 巻 (2000)
- 4 号 p. 475-
- 3 号 p. 321-
- 2 号 p. 163-
- 1 号 p. 1-
52 巻, 2 号
選択された号の論文の10件中1～10を表示しています
- |<
- <
- 1
- >
- >|
-
RONALDO GARCIA, CARLOS GUTIERREZ, JORGE SOTOMAYOR2000 年 52 巻 2 号 p. 163-172
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーIn this paper is studied the configuration of lines of curvature near a Whitney umbrella which is the unique stable singularity for maps of surfaces into R^3. The pattern of such configuration is established and characterized in terms of the 3-jet of the map. The result is used to establish an expression for the Euler-Poincare characteristic in terms of the number of umbilics and umbrellas.抄録全体を表示PDF形式でダウンロード (411K) -
WIESLAW J. OLEDZKI2000 年 52 巻 2 号 p. 173-198
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーWe give a transparent description of the one-fold smooth suspension of Fintushel-Stern's exotic involution on the 4-sphere. Moreover we prove that any two involutions of the 4-sphere are stably (i.e., after one-fold suspension) smoothly conjugated if and only if the corresponding quotient spaces (real homotopy projective spaces) are stably diffeomorphic. We use the Atiyah-Patodi-Singer eta-invariant to detect smooth structures on homotopy projective spaces and prove that any homotopy projective space is detected in this way in dimensions 5 and 6.抄録全体を表示PDF形式でダウンロード (1385K) -
EUGENE V. FERAPONTOV2000 年 52 巻 2 号 p. 199-233
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーTwo basic Lie-invariant forms uniquely defining a generic (hyper)surface in Lie sphere geometry are introduced. Particularly interesting classes of surfaces associated with these invariants are considered. These are the diagonally cyclidic surfaces and the Lie-minimal surfaces, the latter being the extremals of the simplest Lie-invariant functional generalizing the Willmore functional in conformal geometry. K Equations of motion of a special Lie sphere frame are derived, providing a convenient unified treatment of surfaces in Lie sphere geometry. In particular, for diagonallycyclidic surfaces this approach immediately implies the stationary modified Veselov-Novikov equation, while the case of Lie-minimal surfaces reduces in a certain limit to the integrable coupled Tzitzeica system. K In the framework of the canonical correspondence between Hamiltonian systms of hydrodynamic type and hypersurfaces in Lie sphere geometry, it is pointed out that invariants of Lie-geometric hypersurfaces coincide with the reciprocal invariants of hydrodynamic type systems. K Integrable evolutions of surfaces in Lie sphere geometry are introduced. This provides an interpretation of the simplest Lie-invariant functional as the first local conservation law of the (2+1)-dimensional modified Veselov-Novikov hierarchy. K Parallels between Lie sphere geometry and projective differential geometry of surfaces are drawn in the conclusion.抄録全体を表示PDF形式でダウンロード (1399K) -
ALI FARDOUN, ANDREA RATTO2000 年 52 巻 2 号 p. 235-249
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーThe main aim of this paper is to compute the index and the nullity of the identity map of S^n× S^m and S^n× T^m. In order to obtain this we establish a rather general result on the spectrum of the Hodge-Laplacian on k-forms on a product manifold, which could prove useful in other contexts.抄録全体を表示PDF形式でダウンロード (526K) -
GEORGE GASPER, WALTER TREBELS2000 年 52 巻 2 号 p. 251-260
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーSuppose the fractional integration operator I^σ is generated by the sequence {(k+1)-σ } in the setting of Laguerre and Hermite expansions. Then, via projection formulas, the problem of the norm boundedness of I^σ is reduced to the well-known fractional integration on the half-line. A corresponding result with respect to the modified Hankel transform is derived and its connection with the Laguerre fractional integration is indicated.抄録全体を表示PDF形式でダウンロード (399K) -
KATSUHIRO YOSHIJI2000 年 52 巻 2 号 p. 261-270
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーThere exists a Riemannian metric on the real projective space such that the first eigenvalue coincides with that of its Riemannian universal cover, if the dimension is bigger than 2. For the proof, we deform the canonical metric on the real projective space. A similar result is obtained for lens spaces, as well as for closed Riemannian manifolds with Riemannian double covers. As a result, on a non-orientable closed manifold other than the real projective plane, there exists a Riemannian metric such that the first eigenvalue coincides with that of its Riemannian double cover.抄録全体を表示PDF形式でダウンロード (409K) -
XIAOHUAN MO, CAIO J.C. NEGREIROS2000 年 52 巻 2 号 p. 271-282
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーBy using moving frames and directred digraphs, we study invariant (1, 2)-symplectic structures on complex flag manifolds. Let F be a flag manifold with height k-1. We show that there is a k-dimensional family of invariant (1, 2)-symplectic metrics of any parabolic structure on F. We also prove any invariant almost complex structure J on F with height 4 admits an invariant (1, 2)-symplectic metric if and only if J is parabolic or integrable.抄録全体を表示PDF形式でダウンロード (366K) -
YOSHIHISA KITAGAWA2000 年 52 巻 2 号 p. 283-298
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーFor an isometric immersion f of a flat torus into the unit 3-sphere, we show that if the mean curvature of f is not constant, then the immersion f admits a nontrivial isometric deformation preserving the total mean curvature.抄録全体を表示PDF形式でダウンロード (578K) -
QUO-SHIN CHI2000 年 52 巻 2 号 p. 299-308
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーIt was established by X. Mo and the author that the dimension of each irreducible component of the moduli space \mathcal{M}d, g(X) of branched superminimal immersions of degree d from a Riemann surface X of genus g into {C}P^3 lay between 2d-4g+4 and 2d-g+4 for d sufficiently large, where the upper bound was always assumed by the irreducible component of totally geodesic branched superminimal immersions and the lower bound was assumed by all nontotally geodesic irreducible components of \mathcal{M}6, 1(T) for any torus T. It is shown, via deformation theory, in this note that for d=8g+1+3k, k≥q 0, and any Riemann surface X of g≥q 1, the above lower bound is assumed by at least one irreducible component of \mathcal{M}d, g(X).抄録全体を表示PDF形式でダウンロード (417K) -
YONGJIN SONG2000 年 52 巻 2 号 p. 309-319
発行日: 2000/06/01
公開日: 2009/05/22
ジャーナル フリーThe disjoint union of mapping class groups forms a braided monoidal category. We give an explicit expression of braidings in terms of both their actions on the fundamental group of the surface and the standard Dehn twists. This braided monoidal category gives rise to a double loop space. We prove that the action of little 2-cube operad does not extend to the action of little 3-cube operad by showing that the Browder operation induced by 2-cube operad action is nontrivial. A rather simple expression of Reshetikhin-Turaev representation is given for the sixteenth root of unity in terms of matrices with entries of complex numbers. We show by matrix calculation that this representation is symmetric with respect to the braid structure.抄録全体を表示PDF形式でダウンロード (472K)
- |<
- <
- 1
- >
- >|