Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

We will generalize Jaco’s Handle Addition Theorem to the ncompressibility of surfaces on the boundary of 3-manifolds. Several corollaries are given, which show how the theorem can be applied to different situations. 1 The Handle Addition Theorem was first proved by Przytycki [6] in the case when M is a handlebody. In [4] Jaco proved the general version below. Handle Addition Theorem [4] Suppose...

We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In thin manifold, we complex length short closed geodesic. These results quantify filling theorem Brock Bromberg, extend previous authors from finite volume 3-manifolds to any tame 3-manifold. To prove main results, assemble tools Kleinian group theory i...

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures. In this article we explain how to normalize tight contact structures with respect to a fixed triangulation. Using t...

Stable manifolds of saddle points are important in defining the dynamics of smooth nonlinear dynamical systems [1]. The stable manifold theorem for a fixed point states that there are local stable and unstable manifolds tangent to the eigenspaces of the linearised system at the fixed point. The global stable (and unstable) manifold is given by the union of backward (and forward) mappings in tim...

In smooth manifold theory, the notion of a tangent space makes it possible for differentiation to take place on an abstract manifold. In this paper, the notion of a distribution will be presented which makes it possible for integration to take place on an abstract manifold. The first section introduces terminology and builds intuition via an analogy to the concept of integral curves. The second...

A major breakthrough in the theory of topological algorithms occurred in 1992 when Hyam Rubinstein introduced the idea of an almost normal surface. We explain how almost normal surfaces emerged naturally from the study of geodesics and minimal surfaces. Patterns of stable and unstable geodesics can be used to characterize the 2-sphere among surfaces, and similar patterns of normal and almost no...