Quasi-Continuous Vector Fields on RCD Spaces

Concurrent vector fields on Finsler spaces

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

Spaces of Local Vector Fields

Vector fields defined only over a part of a manifold give rise to indexes and to transfers. These local vector fields form a topological space whose relation to configuration spaces was studied by Dusa McDuff, and whose higher dimensional homotopy and homology promise invariants of parametrized families of local vector fields. We show that the assignment of the transfer to the vector field give...

Admissible vector fields and quasi-invariant measures∗

On $beta-$topological vector spaces

We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.  

Orbit spaces of gradient vector fields

We study orbit spaces of generalized gradient vector fields for Morse functions. Typically, these orbit spaces are non-Hausdorff. Nevertheless, they are quite structured topologically and are amenable to study. We show that these orbit spaces are locally contractible. We also show that the quotient map associated to each such orbit space is a weak homotopy equivalence and has the path lifting p...