Topogical equivalence of monotone nonlinear nonautonomous differential equations
Topological and Noether-conservation laws
Topological charges and high dimensional instantons
Topological groups and convex sets homeomorphic to non-separable Hilbert spaces
Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f n: X → X)nεgw such that each f n is -near to the identity map of X and the family f n(X)n∈ω is locally finite...
Topological invariants of isolated complete intersection curve singularities
In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.
Topological Sufficiency of Smooth Map-Germs.
Topological Triviality of Deformations of Functions and Newton Filtrations.
Topological triviality of versal unfoldings of complete intersections
We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities.The algebraic conditions are related to the operation of adjoining powers,...
Topological Type in Families of Germs.
Topologically -determined map germs are topologically cone-like
Topologically nondegenerate functions
Topologie des hypersurfaces pfaffiennes
Topology and closed characteristics of -contact manifolds.
Toroidal Lie group actions on compact Riemannian manifolds and their relations to the fibering problem.
Torsion and the second fundamental form for distributions
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one case generalises the traditional shape operator of Riemannian geometry.
Torsion Tensor and Critical Metrics on Contact (2n + 1)-Manifolds.
Torsions of connections on higher order cotangent bundles
By a torsion of a general connection on a fibered manifold we understand the Frölicher-Nijenhuis bracket of and some canonical tangent valued one-form (affinor) on . Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.
Torsions of connections on tangent bundles of higher order
The torsions of a general connection on the th-order tangent bundle of a manifold are defined as the Frölicher-Nijenhuis bracket of with the natural affinors. The author deduces the basic properties of these torsions. Then he compares them with the classical torsion of a principal connection on the th-order frame bundle of .
Torsions of connections on time-dependent Weil bundles
We introduce the concept of a dynamical connection on a time-dependent Weil bundle and we characterize the structure of dynamical connections. Then we describe all torsions of dynamical connections.
Total bending of vector fields on Riemannian manifolds.