Mostrando recursos 1 - 20 de 2.693

  1. A Geometric Proof of a Result of Takeuchi

    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.

  2. A twisted moment map and its equivariance

    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.

  3. A note on the Kakeya maximal operator and radial weights on the plane

    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.

  4. Wintgen ideal submanifolds of codimension two, complex curves, and Möbius geometry

    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...

  5. Holomorphic submersions onto Kähler or balanced manifolds

    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.

  6. Construction of sign-changing solutions for a subcritical problem on the four dimensional half sphere

    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 $K$.

  7. Convergence of measures penalized by generalized Feynman-Kac transforms

    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.

  8. Homogeneous Ricci soliton hypersurfaces in the complex hyperbolic spaces

    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.

  9. Calabi–Yau 3-folds of Borcea–Voisin type and elliptic fibrations

    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...

  10. The equivariant $K$-theory and cobordism rings of divisive weighted projective spaces

    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...

  11. On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations

    Dias, Fabio Scalco; Tari, Farid
    We initiate in this paper the study of the geometry of the cross-cap in Minkowski 3-space $\mathbb{R}^3_1$. We distinguish between three types of cross caps according to their tangential line being spacelike, timelike or lightlike. For each of these types, the principal plane which is generated by the tangential line and the limiting tangent direction to the curve of self-intersection of the cross-cap plays a key role. We obtain special parametrisations for the three types of cross-caps and consider their affine properties. The pseudo-metric on the cross-cap changes signature along a curve and the singularities of this curve depend on...

  12. Holomorphic equivalence problem for Reinhardt domains and the conjugacy of torus actions

    Shimizu, Satoru
    In this paper, we give an answer to the holomorphic equivalence problem for a basic class of unbounded Reinhardt domains. As an application, we show the conjugacy of torus actions on such a class of Reinhardt domains, and discuss the relation between the holomorphic equivalence problem for Reinhardt domains and the conjugacy of torus actions.

  13. Compact sums of Toeplitz products and Toeplitz algebra on the Dirichlet space

    Lee, Young Joo
    In this paper we consider Toeplitz operators on the Dirichlet space of the ball. We first characterize the compactness of operators which are finite sums of products of two Toeplitz operators. We also characterize Fredholm Toeplitz operators and describe the essential norm of Toeplitz operators. By using these results, we establish a short exact sequence associated with the $C^*$-algebra generated by all Toeplitz operators.

  14. Bowman-Bradley type theorem for finite multiple zeta values

    Saito, Shingo; Wakabayashi, Noriko
    The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between $3,1,\dots,3,1$ add up to a rational multiple of a power of $\pi$. We show that an analogous theorem holds in a very strong sense for finite multiple zeta values, which have been investigated by Hoffman and Zhao among others and recently recast by Zagier.

  15. Codimension one connectedness of the graph of associated varieties

    Nishiyama, Kyo; Trapa, Peter; Wachi, Akihito
    Let $ \pi $ be an irreducible Harish-Chandra $ (\mathfrak{g}, K) $-module, and denote its associated variety by $ \mathcal{AV}(\pi) $. If $ \mathcal{AV}(\pi) $ is reducible, then each irreducible component must contain codimension one boundary component. Thus we are interested in the codimension one adjacency of nilpotent orbits for a symmetric pair $ (G, K) $. We define the notion of orbit graph and associated graph for $ \pi $, and study its structure for classical symmetric pairs; number of vertices, edges, connected components, etc. As a result, we prove that the orbit graph is connected for even nilpotent...

  16. Large deviation principles for generalized Feynman-Kac functionals and its applications

    Kim, Daehong; Kuwae, Kazuhiro; Tawara, Yoshihiro
    Large deviation principles of occupation distribution for generalized Feyn-man-Kac functionals are presented in the framework of symmetric Markov processes having doubly Feller or strong Feller property. As a consequence, we obtain the $L^p$-independence of spectral radius of our generalized Feynman-Kac functionals. We also prove Fukushima's decomposition in the strict sense for functions locally in the domain of Dirichlet form having energy measure of Dynkin class without assuming no inside killing.

  17. A note on Rhodes and Gottlieb-Rhodes groups

    Choi, Kyoung Hwan; Jo, Jang Hyun; Moon, Jae Min
    The purpose of this paper is to give positive answers to some questions which are related to Fox, Rhodes, Gottlieb-Fox, and Gottlieb-Rhodes groups. Firstly, we show that for a compactly generated Hausdorff based $G$-space $(X,x_0,G)$ with free and properly discontinuous $G$-action, if $(X,x_0,G)$ is homotopically $n$-equivariant, then the $n$-th Gottlieb-Rhodes group $G\sigma_n(X,x_0,G)$ is isomorphic to the $n$-th Gottlieb-Fox group $G\tau_n(X/G,p(x_0))$. Secondly, we prove that every short exact sequence of groups is $n$-Rhodes-Fox realizable for any positive integer $n$. Finally, we present some positive answers to restricted realization problems for Gottlieb-Fox groups and Gottlieb-Rhodes groups.

  18. Wedge operations and torus symmetries

    Choi, Suyoung; Park, Hanchul
    A fundamental result of toric geometry is that there is a bijection between toric varieties and fans. More generally, it is known that some classes of manifolds having well-behaved torus actions, say toric objects, can be classified in terms of combinatorial data containing simplicial complexes. ¶ In this paper, we investigate the relationship between the topological toric manifolds over a simplicial complex $K$ and those over the complex obtained by simplicial wedge operations from $K$. Our result provides a systematic way to classify toric objects associated with the class of simplicial complexes obtained from a given $K$ by wedge operations. As...

  19. Isometric deformations of cuspidal edges

    Naokawa, Kosuke; Umehara, Masaaki; Yamada, Kotaro
    Along cuspidal edge singularities on a given surface in Euclidean 3-space $\boldsymbol{R}^3$, which can be parametrized by a regular space curve $\hat\gamma(t)$, a unit normal vector field $\nu$ is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of $\hat\gamma(t)$ is not orthogonal to $\nu$. This genericity is equivalent to the condition that its limiting normal curvature $\kappa_\nu$ takes a non-zero value. In this paper, we show that a given generic (real analytic) cuspidal edge $f$ can be isometrically deformed preserving $\kappa_\nu$ into a cuspidal edge whose singular...

  20. Construction of isolated left orderings via partially central cyclic amalgamation

    Ito, Tetsuya
    We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples of isolated orderings, and give an example of isolated left orderings with various properties which previously known isolated orderings do not have.

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