Related papers: Normal and tangent maps to frontals
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
We introduce new families of quandles that serve as invariants for classifying closed orientable surfaces. These families generalize the classical Dehn quandle and are defined, respectively, on isotopy classes of unoriented closed curves…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…
We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle…
The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.
We introduce a higher dimensional quasiregular map analogous to the trigonometric functions and we use the dynamics of this map to define, for d>1, a partition of d-dimensional Euclidean space into curves tending to infinity such that two…
In this paper, we expand on previous work describing partial derivatives and metric component estimators to define tangent spaces on causal sets. Partial derivative operators are the basis vectors of the tangent space, and the metric…
In this paper, some particular rational maps P_n ---> P_n+1, called quadratic congruences, are studied. They appear in the theory of exceptional vector bundles on projective spaces.
In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an…
We study plane curves over finite fields whose tangent lines at smooth $\mathbb{F}_q$-points together cover all the points of $\mathbb{P}^2(\mathbb{F}_q)$.
The geometry of parallelizable manifolds is presented from the standpoint of regarding it as conventional (e.g., Euclidian or Minkowskian) geometry, when it is described with respect to an anholonomic frame field that is defined on the…
We study the surjectivity of suitable weighted Gaussian maps which provide a natural generalization of the standard Gaussian maps and encode the local geometry of the locus of curves endowed with a higher root of the canonical bundle having…
In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian…
Riemann normal coordinates (RNC) at a regular event $p_0$ of a spacetime manifold $\mathcal{M}$ are constructed by imposing: (i) $g_{\textsf{ab}}|_{p_0}=\eta_{ab}$, and (ii) $\Gamma^\textsf{a}_{\phantom{\textsf a}\textsf{bc}}|_{p_0}=0$.…
Let q be a power of a prime integer p, and let X be a Hermitian variety of degree q+1 in the n-dimensional projective space. We count the number of rational normal curves that are tangent to X at distinct q+1 points with intersection…
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all…
As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically…
A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are quarter-circles, but Tangles comprised of thirds and sixths…
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are…