arXiv research

Sharp characterization of Willmore invariant in higher dimensions.

Characterizes Milnor invariants with limited repetitions.

Invariant covariant derivatives on homogeneous spaces are characterized.

The paper characterizes law-invariant star-shaped risk measures.

In this paper we construct some multi-time geometrical extensions of the KCC-invariants, which characterize a given second-order system of PDEs on the 1-jet space $J^1(T,M)$. A theorem of characterization of these multi-time geometrical KCC-invariants is given.

In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space $J^1(R,M)$. A generalized theorem of characterization of our jet geometrical KCC-invariants is also presented.

In this paper, we give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closure of (cabled) string links. We show that finite type invariants classify string links up to …

This paper characterizes Milnor invariants using diagrammatic methods.

The Cartan equivalence method is applied to provide an invariant characterization of the third-order ordinary differential equation $u'''=f(x,u,u',u'')$ which admits a five-dimensional point symmetry Lie algebra. The invariant characterization is given in terms of the function $f$ in a compact form. A simple procedure …

In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant). We also characterize a function such that there is a hyperbolic angle structure having the function as the edge…

Characterizes values of slice-torus invariants related to knot genus.

In this study, we give the dual characterizations of Mannheim offsets of the ruled surface in terms of their integral invariants and the new characterization of the Mannheim offsets of developable surface. Furthermore, we obtain the relationships between the area of projections of spherical images for Mannheim offsets …

Study characterizes submanifolds in metallic semi-Riemannian manifolds with specific connections.

We give a characterization of conformal classes realizing a compact manifold's Yamabe invariant. This characterization is the analogue of an observation of Nadirashvili for metrics realizing the maximal first eigenvalue, and of Fraser and Schoen for metrics realizing the maximal first Steklov eigenvalue.

Characterizes graphs with leveled embeddings and introduces new graph invariants.

Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction to the slow flow. The focus of this work is on a proposition and discussion of a …

We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen, Beliakova and Wehrli's $s$-invariant. We also study almost positive links, in particular, determine the $s$-invariants of almost positive links. This result suggests that all almost positive links might be strongl…

Study on efficiency in economies with risk-averse agents, finding Pareto optima.

The study characterizes real flag manifolds with invariant generalized almost complex structures.

We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…

Characterizes symmetric Killing tensors on specific Lie groups.

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is lineari…

New method characterizes thin links via Conway spheres and tangle decompositions.

In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescal…

Study invariant Poisson structures on homogeneous manifolds, algebraically and geometrically.

Inspired by the Lichnerowicz-Obata theorem for the first eigenvalue of the Laplacian, we define a new family of invariants $\{Ω_k(g)\}$ for closed Riemannian manifolds. The value of $Ω_k(g)$ delicately reflects the spherical part of the manifold. Indeed, $Ω_1(g)$ and $Ω_2(g)$ characterize the standard sphere.

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are …

New approach finds analytic interpretation of algebraic invariants for balanced metrics.

The study characterizes submanifolds in product spaces.

Curvature measures uniquely determined by invariance under embeddings.

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection. Then we specialize the characterization to the case of a left invariant connecti…

In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzi…

This paper characterizes extensions of augmented racks and constructs invariants for surfaces.

Characterizes invariant contact metric structures on tangent sphere bundles of compact symmetric spaces.

New method to determine parabolic surfaces invariant under Killing fields.

The paper characterizes and examines nilpotent complex structures on stratified Lie algebras.

For a two-dimensional surface in the four-dimensional Euclidean space we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and kappa. The condition k = kappa = 0 characterizes the surfaces consisting of flat points. The minimal surfaces are charac…

In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants expressed as polynomials in $Λ$, the cosmological constant. Using this invariant des…

The paper analyzes the tradeoffs between accuracy and invariance in learning representations.

Zh-construction links virtual links to classical ones, simplifying knot invariants.

We show that the holonomy invariance of a function on the tangent bundle of a manifold, together with very mild regularity conditions on the function, is equivalent to the existence of local parallelisms compatible with the function in a natural way. Thus, in particular, we obtain a characterization of generalized Berw…

We characterize Lorentzian three-dimensional hyper-CR Einstein-Weyl structures in terms of invariants of the associated third order ordinary differential equations.

In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe invariant.

New concept of partial law invariance connects decision theory and financial risk management.

We show that the local equivalence problem for second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also show that, modulo Cartan duality and point transformations, the Painlevé-I equati…

The paper explores non-convex risk measures and their characterizations.

In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.

If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the manifold and its boundary. So essentially, Euler characteristic is the unique inv…