Higher order almost tangent geometry and non-autonomous Lagrangian dynamics
Higher order Cartan connections.
Higher order Cartan connections
A Cartan connection associated with a pair is defined in the usual manner except that only the injectivity of is required. For an -th order connection associated with a bundle morphism the concept of Cartan order is defined, which for , and coincides with the classical definition. Results are obtained concerning the Cartan order of -th order connections that are the product of first order (Cartan) connections.
Higher order Codazzi tensors on conformally flat spaces.
Higher order connections.
Higher order contact of real curves in a real hyperquadric
Higher order contact of real curves in a real hyperquadric. II
Let be an Hermitian quadratic form, of maximal rank and index , defined over a complex vector space . Consider the real hyperquadric defined in the complex projective space by Let be the subgroup of the special linear group which leaves invariant and the distribution defined by the Cauchy Riemann structure induced over . We study the real regular curves of constant type in , tangent to , finding a complete system of analytic invariants for two curves to be locally equivalent...
Higher order frames and linear connections
Higher order geodesic symmetries
Higher order Ossermann pseudo-Riemannian manifolds of neutral signature .
Higher order Schwarzian derivatives in interval dynamics
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive up...
Higher order torsions of manifolds with connection
Higher order torsions of spaces with Cartan connection
Higher order valued reduction theorems for classical connections
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Higher-genus Chen-Gackstatter surfaces and the Weierstrass representation for surfaces of infinite genus.
Higher-order differential equations represented by connections on prolongations of a fibered manifold.
The main goal of the present work is a generalization of the ideas, constructions and results from the first and second-order situation, studied in [63], [64] to that of an arbitrary finite-order one. Moreover, the investigation extends the ideas of [65] from the one-dimensional base X corresponding to O.D.E.
Highly Connected Taut Submanifolds.
High-order angles in almost-Riemannian geometry
Let and be two smooth vector fields on a two-dimensional manifold . If and are everywhere linearly independent, then they define a Riemannian metric on (the metric for which they are orthonormal) and they give to the structure of metric space. If and become linearly dependent somewhere on , then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way...
Hilbert volume in metric spaces. Part 1
We introduce a notion of Hilbertian n-volume in metric spaces with Besicovitch-type inequalities built-in into the definitions. The present Part 1 of the article is, for the most part, dedicated to the reformulation of known results in our terms with proofs being reduced to (almost) pure tautologies. If there is any novelty in the paper, this is in forging certain terminology which, ultimately, may turn useful in an Alexandrov kind of approach to singular spaces with positive scalar curvature [Gromov...