Related papers: Shape spaces of nonlinear flags
Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…
Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering the space variable-independent solutions only. This simplification leads to a degenerate…
Several Riemannian metrics and families of Riemannian metrics were defined on the manifold of Symmetric Positive Definite (SPD) matrices. Firstly, we formalize a common general process to define families of metrics: the principle of…
We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant…
Below the roughening temperature, the equilibrium crystal shape (ECS) is composed of both facets and a smoothly curved surface. As for the ``normal'' profile (perpendicular to the facet contour), the ECS has the exponent 3/2 which is…
Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, we construct a family of paracontact metric structures. We prove that this…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
Bending the edge of a thin elastic material promotes rigidity far from its clamped boundary. However, this curvature-induced rigidity can be overwhelmed by gravity or other external loading, resulting in elastic buckling and large…
In this paper, generalizing the techniques of Bour's theorem, we prove that every generic cuspidal edge, more generally, generic $n$-type edge, which is invariant under a helicoidal motion in Euclidean $3$-space admits non-trivial isometric…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.
This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional…
Geometric frameworks for analyzing curves are common in applications as they focus on invariant features and provide visually satisfying solutions to standard problems such as computing invariant distances, averaging curves, or registering…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by \"Ozdamar and Hacisaliho\u{g}lu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve…
Consider a compact manifold $M$ with smooth boundary $\partial M$. Suppose that $g$ and $\tilde{g}$ are two Riemannian metrics on $M$. We construct a family of metrics on $M$ which agrees with $g$ outside a neighborhood of $\partial M$ and…
A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved…