Related papers: Characterization of Closed Vector Fields in Finsle…

This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…

In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(\alpha,\beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the…

There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of $I$-invariant projective vector fields. The sub-algebra of the $C$-projective vector fields, leaving…

We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…

A projective parameter of a geodesic on a Finsler space is defined to be solution of a certain ODE. Using projective parameter and Funk metric, one can construct a projectively invariant intrinsic pseudo-distance on a Finsler space. In the…

Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models.…

Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…

We investigate what henselian valuations on ordered fields are definable in the language of ordered rings. This leads towards a systematic study of the class of ordered fields which are dense in their real closure. Some results have…

We first present the natural definitions of the horizontal differential, the divergence (as an adjoint operator), and a $p$-harmonic form on a Finsler manifold. Next, we prove a Hodge-type theorem for a Finsler manifold in the sense that a…

We prove the existence of real Picard-Vessiot extensions for real partial differential fields with real closed field of constants. We establish a Galois correspondence theorem for these Picard-Vessiot extensions and characterize real…

Skew-symmetric differential forms play an unique role in mathematics and mathematical physics. This relates to the fact that closed exterior skew-symmetric differential forms are invariants. The concept of "Exterior differential forms" was…

Let R be a sufficiently saturated o-minimal expansion of a real closed field, let O be the convex hull of the rationals in R, and let st: O^n \to \mathbb{R}^n be the standard part map. For X \subseteq R^n define st(X):=st(X \cap O^n). We…

We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional…

The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60…

We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of…

We determine all Finsler metrics of Randers type for which the Riemannian part is a scalar multiple of the Euclidean metric, on an open subset of the Euclidean plane, whose geodesics are circles. We show that the Riemannian part must be of…

The Poincar\'e-Hopf Theorem is a conservation law for real-analytic vector fields, which are tangential to a closed surface (such as a torus or a sphere). The theorem also governs real-analytic vector fields, which are tangential to…

This note provides an affirmative answer to a question of Viterbo concerning the existence of nondiffeomorphic contact forms that share the same Reeb vector field. Starting from an observation by Croke-Kleiner and Abbondandolo that such…

We consider shadowing properties for vector fields corresponding to different type of reparametrisations. We give an example of a vector field which has the oriented shadowing properties, but does not have the standard shadowing property.

We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…