$2k$-regular maps on smooth manifolds

On path decompositions of 2k-regular graphs

Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partitioned into ⌈n/2⌉ paths. Let Gk be the class of all 2k-regular graphs of girth at least 2k − 2 that admit a pair of disjoint perfect matchings. In this work, we show that Gallai’s conjecture holds in Gk, for every k ≥ 3. Further, we prove that for every graph G in Gk on n vertices, there exists a par...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Equivariant Lefschetz Maps for Simplicial Complexes and Smooth Manifolds

Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of Lefschetz numbers to equivariant K-homology classes. We compute the Lefschetz invariants for self-maps of finite-dimensional simplicial complexes and of self-maps o...

Geodesic Manifolds with a Transitive Subset of Smooth Bilipschitz Maps

This paper is connected with the problem of describing path metric spaces which are homeomorphic to manifolds and biLipschitz homogeneous, i.e., whose biLipschitz homeomorphism group acts transitively. Our main result is the following. LetX = G/H be a homogeneous space of a Lie group G, and let d be a geodesic distance on X inducing the same topology. Suppose there exists a subgroup GS of G whi...

Harmonic Maps on Kenmotsu Manifolds

We study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.