Related papers: Tangent Developable Orbit Space of an Octupole
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in…
In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces…
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…
Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by…
We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions.…
Consider a limit space $(M_\alpha,g_\alpha,p_\alpha)\stackrel{GH}{\rightarrow} (Y,d_Y,p)$, where the $M_\alpha^n$ have a lower Ricci curvature bound and are volume noncollapsed. The tangent cones of $Y$ at a point $p\in Y$ are known to be…
We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits…
We examine the moduli space of oriented locally homogeneous manifolds of Type A which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at…
While the tangent space to an equisingular family of curves can be discribed by the sections of a twisted ideal sheaf, this is no longer true if we only prescribe the multiplicity which a singular point should have. However, it is still…
We describe a new class of supersymmetric orientifolds which combine the world-sheet parity transformation with a complex conjugation in the compact directions. As an example, we investigate in detail the orientifold of the Z_3 toroidal…
We study the discriminant of a degree 4 extension given by a deformed bidouble cover, i.e., by equations z^2= u + a w, w^2= v + bz. We first show that the discriminant surface is a quartic which is cuspidal on a twisted cubic, i.e.,is the…
We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\mathrm{OG}10$ type associated to…
We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical…
The Hessian of a general cubic surface is a nodal quartic surface, hence its desingularisation is a K3 surface. We determine the transcendental lattice of the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt points…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…
The secular approximation for the evolution of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple-star systems. In this approximation the orbits may change shape and…
For each connected alternating tangle, we provide an infinite family of non-left-orderable L-spaces. This gives further support for Conjecture [3] of Boyer, Gordon, and Watson that is a rational homology 3-sphere is an L-space if and only…
We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature $K$ satisfies \begin{equation*} K\Delta K - \|\nabla K\|^2-4K^3 = 0. \end{equation*} These surfaces are referred to as rotational Ricci…
In this article, we study spacelike and timelike rotational surfaces in a 3--dimensional de Sitter space $\mathbb{S}^3_1$ which are the orbit of a regular curve under the action of the orthogonal transformation of 4--dimensional Minkowski…
We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…