The convex cone SC1 SLip(X) of real-valued smooth semi-Lipschitz functions on a Finsler manifold X is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of X. In this work ...

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological ...

In this work, we consider piecewise smooth vector fields X defined in R n \ ∑, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε.η , ε,η > ...

In this paper we study functions and vector fields with isolated singularities on a C(ℂPn)-singular manifold. In general, a C(ℂPn)-singular manifold is obtained from a smooth (2n + 1)-manifold with boundary which is a ...

This paper studies structural properties of locally symmetric submanifolds. One of the main result states that a locally symmetric submanifold M of R-n admits a locally symmetric tangential parametrization in an appropriately ...

We deal with piecewise-smooth differential systems ż= X(z) , z= (x, y) ∈ ℝ× ℝn − 1, with switching occurring in a codimension one smooth surface Σ. A regularization of X is a 1-parameter family of smooth vector fields Xδ,δ ...

In this work, we will initially present generalized bundles, a concept developed by Fadell with the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the context of smooth manifolds ...

In this paper we study functions and vector fields with isolated singularities on a C(CPn)-singular manifold. In general, a C(CPn)-singular manifold is obtained from a smooth (2n+1) -manifold with boundary which is a ...