Mostrando recursos 1 - 20 de 22

  1. Graded Lie Agebroids of Poisson Almost Commutative Algebras

    Ngakeu, Ferdinand
    We introduce and study the notion of abelian groups graded Lie algebroid structures on almost commutative algebras $\mathcal A$ and show that any graded Poisson bracket on $\mathcal A$ induces a graded Lie algebroid structure on the $\mathcal A$-module of 1-forms on $\mathcal A$ as in the classical Poisson manifolds. We also derive from our formalism the graded Poisson cohomology.

  2. On Symplectic Dynamics

    Tchuiaga, Stéphane
    This paper continues to carry out a foundational study of Banyaga's topologies of a closed symplectic manifold $(M,\omega)$ [4]. Our intention in writing this paper is to work out several “symplectic analogues” of some results found in the study of Hamiltonian dynamics. By symplectic analogue, we mean if the first de Rham's group (with real coefficients) of the manifold is trivial, then the results of this paper reduce to some results found in the study of Hamiltonian dynamics. Especially, without appealing to the positivity of the symplectic displacement energy, we point out an impact of the $L^\infty-$version of Hofer-like length...

  3. About the Degenerate Spectrum of the Tension Field for Mappings into a Symmetric Riemannian Manifold

    Kourouma, Moussa
    Let $(M,g)$ and $(N,h)$ be compact Riemannian manifolds, where $(N,h)$ is symmetric, $v\in W^{1,2}((M,g),(N,h))$, and $\tau $ is the tension field for mappings from $(M,g)$ into $(N,h)$. We consider the nonlinear eigenvalue problem $\tau (u)-\lambda \exp _{u}^{-1}v=0$, for $u$ $\in W^{1,2}(M,N)$ such that $u_{\left\vert \partial M\right. }=v_{\left\vert \partial M\right.}$, and $\lambda \in \mathbb{R}$. We prove, under some assumptions, that the set of all $\lambda $, such that there exists a solution $(u,\lambda )$ of this problem and a non trivial Jacobi field $V$ along $u$, is contained in $\mathbb{R}_{+}$, is countable, and has no accumulation point in $\mathbb{R}$. This result...

  4. On Commutativity of Prime Γ-Rings with $θ$-Derivations

    Huang, Shuliang; Rehman, Nadeem ur
    Let $M$ be a prime $\Gamma-$ring, $I$ a nonzero ideal, $\theta$ an automorphism and $d$ a $\theta-$derivation of $M$. In this article we have proved the following result: (1) If $d([x,y]_{\alpha})=\pm([x,y]_{\alpha})$ or $d((x\circ y)_{\alpha})=\pm((x\circ y)_{\alpha})$ for $x, y\in I; \alpha\in \Gamma$, then $M$ is commutative. (2) Under the hypothesis $d\theta=\theta d$ and $Char M\neq2$, if $(d(x)\circ d(y))_{\alpha}=0$ or $[d(x),d(y)]_{\alpha}=0$ for all $x, y\in I;\alpha\in \Gamma$, then $M$ is commutative. (3) If $d$ acts as a homomorphism or an anti-homomorphism on $I$, then $d=0$ or $M$ is commutative. Moreover, an example is given to demonstrate that the primeness imposed on the...

  5. Existence of Solutions of Some Nonlinear $φ$-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions

    Goli, Charles Etienne; Adje, Assohoun
    We study the existence of solutions of the quasilinear equation $$(D(u(t))\phi(u'(t)))'=f(t,u(t),u'(t)),\qquad a.e. \;\;t\in [0,T],$$ subject to nonlinear Neumann-Steklov boundary conditions on $[0,T]$, where $\phi: (-a,a)\rightarrow \mathbb{R}$ (for $0 < a < \infty$) is an increasing homeomorphism such that $\phi(0)=0$, $f:[0,T]\times\mathbb{R}^{2} \rightarrow \mathbb{R}$ a $L^1$-Carathéodory function, $D$ : $\mathbb{R}\longrightarrow (0,\infty)$ is a continuous function. Using topological methods, we obtain existence and multiplicity results.

  6. Hammerstein Equations with Lipschitz and Strongly Monotone Mappings in Classical Banach spaces

    Diop, C.; Sow, T. M. M.; Djitte, N.; Chidume, C. E.
    Let $E$ be a Banach space either $l_p$ or $L_p$ or $W^{m,p}$, $1 < p < \infty$, with dual $E^*$, and let $F :E\mapsto E^*$, $K: E^*\mapsto E $ be Lipschitz and strongly monotone mappings with $D(K)=R(F)=E^*$. Assume that the Hammerstein equation $u+KFu=0$ has a unique solution $\bar u$. For given $u_1\in E$ and $v_1\in E^*$, let $\{u_n\}$ and $\{v_n\}$ be sequences generated iteratively by: $u_{n+1} = J^{-1}(Ju_n -\lambda(Fu_n-v_n)),\,\,\,n\geq 1$ and $v_{n+1} = J(J^{-1}v_n-\lambda(Kv_n+u_n)),\,\,\,n\geq 1$, where $J$ is the duality mapping from $E$ into $E^*$ and $\lambda$ is a positive real number in $(0,1)$ satisfying suitable conditions. Then it is...

  7. An Example Concerning Hamiltonian Groups of Self Product II

    Hu, S.; Lalonde, F.
    We describe the natural identification of $FH_*(X \times X, \triangle; \omega \oplus \omega)$ with $FH_*(X, \omega)$. Under this identification, we show that the extra elements in ${\rm Ham}(X \times X, \omega \oplus \omega)$ found in [3], for $X = (S^2 \times S^2, \omega_0 \oplus \lambda \omega_0)$ for $\lambda > 1$, do not define new invertible elements in $FH_*(X, \omega)$.

  8. An Example Concerning Hamiltonian Groups of Self Product I

    Hu, S.; Lalonde, F.
    We show that $(S^2\times S^2, \omega_0 \oplus \lambda\omega_0)$, with $\lambda > 1$, is an example of symplectic manifold $(X, \omega)$ such that the $\pi_1{\rm Ham}(X \times X, \omega\oplus \omega)$ contains extra elements than those from $\pi_1{\rm Ham}(X, \omega) \times \pi_1{\rm Ham}(X, \omega)$.

  9. KV-Cohomology and Differential Geometry of Affinely Flat Manifolds. Information Geometry

    Nguiffo Boyom, M.; Ngakeu, F.; Byande, P. M.; Wolak, R.
    This paper is devoted to the socalled twisted cohomology of Koszul-Vinberg algebras. We discuss relationships between the twisted cohomology of Koszul-Vinberg algebras and Chevalley-Eilenberg cohomology of the commutator algebra of these algebras. We also discuss some geometry applications of these relationships. For instance we obtain some homological criteria for hyberbolicity and for completeness of locally flat manifolds. We also discuss some topics which are related to twisted cohomology. In particular, we use some techniques of information geometry to discuss canonical representations of locally flat connections.

  10. Integration of Conformal Jacobi Fibrations and Prequantization of Poisson Fibrations

    Wade, A.
    We show that integrable conformal Jacobi fibrations are in onetoone correspondence with sourcesimply connected fibered conformal contact groupoids. We also prove that prequantizable Poisson fibrations give rise to Jacobi fibrations. In addition, sourcesimply connected symplectic groupoids associated to prequantizable and integrable Poisson fibrations are also prequantizable.

  11. Two Families of Affine Osserman Connections on 3-Dimensional Manifolds

    Diallo, A. S.; Hassirou, M.
    The aim of this note is to study the Osserman condition on two families affine connections. As applications, examples of affine Osserman connections which are Ricci flat but not flat are given.

  12. Three Approaches to Morse-Bott Homology

    Hurtubise, D. E.
    In this paper we survey three approaches to computing the homology of a finite dimensional compact smooth closed manifold using a Morse-Bott function and discuss relationships among the three approaches. The first approach is to perturb the function to a Morse function, the second approach is to use moduli spaces of cascades, and the third approach is to use the Morse-Bott multicomplex. With respect to an explicit perturbation (which can be used to derived the Morse-Bott inequalities), the first two approaches yield the same chain complex up to sign. The third approach is fundamentally different. It combines singular cubical chains...

  13. $\cal D$-Homothetic Warping and Applications to Geometric Structures and Cosmology

    Blair, D. E.
    It is a great pleasure for me to dedicate this paper to Professor Augustin Banyaga in recognition of both his collegiality and his many contributions to symplectic and contact geometry.

  14. Sasakian Metrics with an Additional Contact Structure

    Drăghici, T.; Rukimbira, P.
    The question of whether a Sasakian metric can admit an additional compatible ($K$)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some extensions of this result are obtained, mainly in dimensions 3 and 5.

  15. Sasakian Manifolds with Perfect Fundamental Groups

    Boyer, C. P.; Tønnesen-Friedman, C. W.
    Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions $\geq 3$. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki-Einstein and Sasaki$\eta$Einstein metrics.

  16. My Life with Augustin

    Chaperon, M.
    This is a very brief and partial account of Augustin's mathematics and our common interests. In the end is presented some recent work of mine whose birth he encouraged.

  17. An Elementary Symmetry-Based Derivation of the Heat Kernel on Heisenberg Group

    Wafo Soh, C.; Diatta, B.; Ndogmo, J. C.
    Using symmetry arguments, we propose a simple derivation of a fundamental solution of the operator $\partial_t \Delta_H$ in which $\Delta_H$ is Kohn-Laplace operator on the Heisenberg group $H^{2n+1}$. Our derivation extends that of Craddock and Lennox [J. Differential Equations 232(2007), 652-674]. Indeed, these authors solved the same problem by employing a symmetry approach in the case $n=1$ . We demonstrate that the case $n=1$ is quite peculiar from a symmetry standpoint and the extension of symmetry arguments to the case $n>1$ requires some intermediate results.

  18. Sur les Feuilletages de Lie Nilpotents

    Dathe, H.; Ndiaye, A.
    On construit sur une variété compacte un feuilletage de Lie nilpotent et non abélien de codimension 4 qui n'admet pas de déformation résoluble non nilpotente.

  19. Bonnet Pairs of Surfaces in Minkowski Space

    Grantcharov, G.; Salom, R.
    We review some results about Bonnet pairs in Minkowski space obtained using split quaternions and split complex numbers. We present also an example of Bonnet pairs of minimal immersed timelike tori with umbilical points. Such examples do not exists in the Euclidean space.

  20. $(q;l,\lambda)$-Deformed Heisenberg Algebra: Coherent States, Their Statistics and Geometry

    Bukweli-Kyemba, J. D.; Hounkonnou, M. N.
    The Heisenberg algebra is deformed with the set of parameters $\{q, l,\lambda\}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the subPoissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.

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