Amalgamations of homogeneous Riemannian spaces
A-manifolds on a principal torus bundle over an almost Hodge A-manifold base
An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇XXRic(X,X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds
Amenable Groups and Stabilizers of Measures on the Boundary of a Hadamard Manifold.
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...
An algebraic characterization of affine manifolds with -structure satisfying a homogeneity condition.
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An almost paracontact structure on the indicatrix bundle of a Finsler space.
An analog of the Vaisman-Molino cohomology for manifolds modelled on some types of modules over Weil algebras and its application.
An analogy of Tian-Todorov theorem on deformations of CR-structures
An anti-Kählerian Einstein structure on the tangent bundle of a space form
In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian structures...
An application of Lie groupoids to a rigidity problem of 2-step nilmanifolds
We study a problem of isometric compact 2-step nilmanifolds using some information on their geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric and is a cocompact discrete subgroup of isometries of . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable factorization...
An application of twistor theory to the non-hyperbolicity of certain compact symplectic Kähler manifolds.
An arithmetic Hilbert–Samuel theorem for pointed stable curves
Let be an arithmetic ring of Krull dimension at most and a pointed stable curve. Write . For every integer , the invertible sheaf inherits a singular hermitian structure from the hyperbolic metric on the Riemann surface . In this article we define a Quillen type metric on the determinant line
An Arzela-Ascoli theorem for immersed submanifolds
The classical Arzela-Ascoli theorem is a compactness result for families of functions depending on bounds on the derivatives of the functions, and is of invaluable use in many fields of mathematics. In this paper, inspired by a result of Corlette, we prove an analogous compactness result for families of immersed submanifolds which depends only on bounds on the derivatives of the second fundamental forms of these submanifolds. We then show how the result of Corlette may be obtained as an immediate...
An Eigenvalue Pinching Theorem.
An elementary formula for the Fenchel-Nielsen twist.
An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties.
An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties
An equichordal characterization of round spheres.
An equivalence theorem for submanifolds of higher codimensions
For a submanifold of of any codimension the notion of type number is introduced. Under the assumption that the type number is greater than 1 an equivalence theorem is proved.