Recursos de colección
Project Euclid (Hosted at Cornell University Library) (192.674 recursos)
Tohoku Mathematical Journal
Tohoku Mathematical Journal
Wang, Peng
The family of Willmore immersions from a Riemann surface into $S^{n+2}$ can be
divided naturally into the subfamily of Willmore surfaces conformally equivalent
to a minimal surface in $\mathbb{R}^{n+2}$ and those which are not conformally
equivalent to a minimal surface in $\mathbb{R}^{n+2}$. On the level of their
conformal Gauss maps into
$Gr_{1,3}(\mathbb{R}^{1,n+3})=SO^+(1,n+3)/SO^+(1,3)\times SO(n)$ these two
classes of Willmore immersions into $S^{n+2}$ correspond to conformally harmonic
maps for which every image point, considered as a 4-dimensional Lorentzian
subspace of $\mathbb{R}^{1,n+3}$, contains a fixed lightlike vector or where it
does not contain such a ``constant lightlike vector''. Using the loop group
formalism for the construction of Willmore immersions we characterize in this
paper...
Asuke, Taro
The derivatives of the Bott class and those of the Godbillon-Vey class with
respect to infinitesimal deformations of foliations, called infinitesimal
derivatives, are known to be represented by a formula in the projective
Schwarzian derivatives of holonomies [3], [1]. It is recently shown that these
infinitesimal derivatives are represented by means of coefficients of transverse
Thomas-Whitehead projective connections [2]. We will show that the formula can
be also deduced from the latter representation.
Inoguchi, Jun-ichi; Munteanu, Marian Ioan
It is an interesting question whether a given equation of motion has a periodic
solution or not, and in the positive case to describe it. We investigate
periodic magnetic curves in elliptic Sasakian space forms and we obtain a
quantization principle for periodic magnetic flowlines on Berger spheres. We
give a criterion for periodicity of magnetic curves on the unit sphere
${\mathbb{S}}^3$.
Inaba, Kazumasa; Ishikawa, Masaharu; Kawashima, Masayuki; Nguyen, Tat Thang
In this paper, we study deformations of Brieskorn polynomials of two variables
obtained by adding linear terms consisting of the conjugates of complex
variables and prove that the deformed polynomial maps have only indefinite fold
and cusp singularities in general. We then estimate the number of cusps
appearing in such a deformation. As a corollary, we show that a deformation of a
complex Morse singularity with real linear terms has only indefinite folds and
cusps in general and the number of cusps is 3.
Morishita, Masanori; Takakura, Yu; Terashima, Yuji; Ueki, Jun
Based on the analogies between knot theory and number theory, we study a
deformation theory for ${\rm SL}_2$-representations of knot groups, following
after Mazur's deformation theory of Galois representations. Firstly, by
employing the pseudo-${\rm SL}_2$-representations, we prove the existence of the
universal deformation of a given ${\rm SL}_2$-representation of a finitely
generated group $\Pi$ over a perfect field $k$ whose characteristic is not 2. We
then show its connection with the character scheme for ${\rm
SL}_2$-representations of $\Pi$ when $k$ is an algebraically closed field. We
investigate examples concerning Riley representations of 2-bridge knot groups
and give explicit forms of the universal deformations. Finally we discuss the
universal deformation of...
Roques, Julien
The guiding thread of the present work is the following result, in the vain of
Grothendieck's conjecture for differential equations : if the reduction modulo
almost all prime $p$ of a given linear Mahler equation with coefficients in
$\mathbb{Q}(z)$ has a full set of algebraic solutions, then this equation has a
full set of rational solutions. The proof of this result, given at the very end
of the paper, relies on intermediate results of independent interest about
Mahler equations in characteristic zero as well as in positive
characteristic.
Mihai, Ion
The generalized Wintgen inequality was conjectured by De Smet, Dillen,
Verstraelen and Vrancken in 1999 for submanifolds in real space forms. It is
also known as the DDVV conjecture. It was proven recently by Lu (2011) and by Ge
and Tang (2008), independently. The present author established a generalized
Wintgen inequality for Lagrangian submanifolds in complex space forms in 2014.
In the present paper we obtain the DDVV inequality, also known as generalized
Wintgen inequality, for Legendrian submanifolds in Sasakian space forms. Some
geometric applications are derived. Also we state such an inequality for contact
slant submanifolds in Sasakian space forms.
Okawa, Shinnosuke
We prove that a projective surface of globally $F$-regular type defined over a
field of characteristic zero is of Fano type.
Kariyama, Kazutoshi
Let $F$ be a non-Archimedean local field, and let $G$ be an inner form of
$\mathrm{GL}_N(F)$ with $N \ge 1$. Let $\boldsymbol{\mathrm{JL}}$ be the
Jacquet--Langlands correspondence between $\mathrm{GL}_N(F)$ and $G$. In this
paper, we compute the invariant $s$ associated with the essentially
square-integrable representation $\boldsymbol{\mathrm{JL}}^{-1}(\rho)$ for a
cuspidal representation $\rho$ of $G$ by using the recent results of Bushnell
and Henniart, and we restate the second part of a theorem given by Deligne,
Kazhdan, and Vignéras in terms of the invariant $s$. Moreover, by using
the parametric degree, we present a proof of the first part of the theorem.
Gilkey, Peter; Kim, Chan Yong; Park, JeongHyeong
We use the solution space of a pair of ODEs of at least second order to construct
a smooth surface in Euclidean space. We describe when this surface is a proper
embedding which is geodesically complete with finite total Gauss curvature. If
the associated roots of the ODEs are real and distinct, we give a universal
upper bound for the total Gauss curvature of the surface which depends only on
the orders of the ODEs and we show that the total Gauss curvature of the surface
vanishes if the ODEs are second order. We examine when the surfaces are
asymptotically minimal.
Quast, Peter
In 1984 Masaru Takeuchi showed that every real form of a hermitian symmetric space of
compact type is a symmetric $R$-space and vice-versa. In this note we present a geometric
proof of this result.
Hashimoto, Takashi
Let $G$ be a linear connected complex reductive Lie group. The purpose of this
paper is to construct a $G$-equivariant symplectomorphism in terms of local
coordinates from a holomorphic twisted cotangent bundle of the generalized flag
variety of $G$ onto the semisimple coadjoint orbit of $G$. As an application,
one can obtain an explicit embedding of a noncompact real coadjoint orbit into
the twisted cotangent bundle.
Saito, Hiroki; Sawano, Yoshihiro
We obtain an estimate of the operator norm of the weighted Kakeya
(Nikodým) maximal operator without dilation on $L^2(w)$. Here we assume
that a radial weight $w$ satisfies the doubling and supremum condition. Recall
that, in the definition of the Kakeya maximal operator, the rectangle in the
supremum ranges over all rectangles in the plane pointed in all possible
directions and having side lengths $a$ and $aN$ with $N$ fixed. We are
interested in its eccentricity $N$ with $a$ fixed. We give an example of a
non-constant weight showing that $\sqrt{\log N}$ cannot be removed.
Li, Tongzhu; Ma, Xiang; Wang, Changping; Xie, Zhenxiao
Wintgen ideal submanifolds in space forms are those ones attaining the equality
pointwise in the so-called DDVV inequality which relates the scalar curvature,
the mean curvature and the scalar normal curvature. Using the framework of
Möbius geometry, we show that in the codimension two case, the mean
curvature spheres of the Wintgen ideal submanifold correspond to a 1-isotropic
holomorphic curve in a complex quadric. Conversely, any 1-isotropic complex
curve in this complex quadric describes a 2-parameter family of spheres whose
envelope is always a Wintgen ideal submanifold of codimension two at the regular
points. Via a complex stereographic projection, we show that our
characterization is equivalent to Dajczer and...
Alessandrini, Lucia
We study many properties concerning weak Kählerianity on compact complex
manifolds which admits a holomorphic submersion onto a Kähler or a
balanced manifold. We get generalizations of some results of Harvey and Lawson
(the Kähler case), Michelsohn (the balanced case), Popovici (the sG case)
and others.
Ghoudi, Rabeh; Ould Bouh, Kamal
This paper is devoted to studying the nonlinear problem with subcritical exponent
$(S_\varepsilon) : -\Delta_g u+2u = K|u|^{2-\varepsilon}u$, in $ S^4_+ $,
${\partial u}/{\partial\nu} =0$, on $\partial S^4_+,$ where $g$ is the standard
metric of $S^4_+$ and $K$ is a $C^3$ positive Morse function on
$\overline{S_+^4}$. We construct some sign-changing solutions which blow up at
two different critical points of $K$ in interior. Furthermore, we construct
sign-changing solutions of $(S_\varepsilon)$ having two bubbles and blowing up
at the same critical point of $K$.
Kim, Daehong; Matsuura, Masakuni
We prove the existence of limiting laws for symmetric stable-like processes
penalized by generalized Feynman-Kac functionals and characterize them by the
gauge functions and the ground states of Schrödinger type operators.
Hashinaga, Takahiro; Kubo, Akira; Tamaru, Hiroshi
A Lie hypersurface in the complex hyperbolic space is an orbit of a cohomogeneity
one action without singular orbit. In this paper, we classify Ricci soliton Lie
hypersurfaces in the complex hyperbolic spaces.
Cattaneo, Andrea; Garbagnati, Alice
We consider Calabi–Yau 3-folds of Borcea–Voisin type, i.e. Calabi–Yau 3-folds
obtained as crepant resolutions of a quotient $(S\times E)/(\alpha_S\times
\alpha_E)$, where $S$ is a K3 surface, $E$ is an elliptic curve, $\alpha_S\in
\operatorname{Aut}(S)$ and $\alpha_E\in \operatorname{Aut}(E)$ act on the period
of $S$ and $E$ respectively with order $n=2,3,4,6$. The case $n=2$ is very
classical, the case $n=3$ was recently studied by Rohde, the other cases are
less known. First, we construct explicitly a crepant resolution, $X$, of
$(S\times E)/(\alpha_S\times \alpha_E)$ and we compute its Hodge numbers; some
pairs of Hodge numbers we found are new. Then, we discuss the presence of
maximal automorphisms and of a point with maximal...
Harada, Megumi; Holm, Tara S.; Ray, Nigel; Williams, Gareth
We apply results of Harada, Holm and Henriques to prove that the Atiyah-Segal
equivariant complex $K$-theory ring of a divisive weighted projective space
(which is singular for non-trivial weights) is isomorphic to the ring of
integral piecewise Laurent polynomials on the associated fan. Analogues of this
description hold for other complex-oriented equivariant cohomology theories, as
we confirm in the case of homotopical complex cobordism, which is the universal
example. We also prove that the Borel versions of the equivariant $K$-theory and
complex cobordism rings of more general singular toric varieties, namely those
whose integral cohomology is concentrated in even dimensions, are isomorphic to
rings of appropriate piecewise formal power...