Isometry - invariant geodesics with Lipschitz obstacle 1
نویسندگان
چکیده
Given a linear isometry A0 : Rn → Rn of finite order on Rn , a general 〈A0〉-invariant closed subset M of Rn is considered with Lipschitz boundary. Under suitable topological restrictions the existence of A0-invariant geodesics of M is proven.
منابع مشابه
Isometry-invariant geodesics and the fundamental group
We prove that on closed Riemannian manifolds with infinite abelian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true if the fundamental group is infinite cyclic. We also formulate a generalization of the isometry-invariant geodesics problem, and a generalization of the cele...
متن کاملIsometry-invariant Geodesics and Nonpositive Derivations of the Cohomology
We introduce a new class of zero-dimensional weighted complete intersections, by abstracting the essential features of Q-cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a 1-connected closed manifold M with H(M, Q) belonging to this class, every isometry has a non-trivial invariant geodesic, for any metric on M . We use Qsurgery to construc...
متن کاملRiemannian Supergeometry
Motivated by Zirnbauer [Zir 1996], we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the Lie theoretical viewpoint are introduced, e.g. geodesics, isometry groups and invariant metrics on Lie supergroups and homogeneous superspaces.
متن کاملA new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces
In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...
متن کاملAsymptotic geometry and growth of conjugacy classes of nonpositively curved manifolds
Let X be a Hadamard manifold and Γ ⊂ Isom(X) a discrete group of isometries which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the limit set of Γ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessarily compact or finite volume manifolds.
متن کامل