Stable mappings of 3-manifolds into the plane

Stable Maps of 3-manifolds into the Plane and Their Quotient Spaces

We study stable maps / : M —*U of closed orientable 3-manifolds M into the plane using their quotient spaces, which are defined to be the spaces of the connected components of/-fibres and which are known to be 2-dimensional polyhedra. We show that every 3-manifold admits a stable map whose quotient space is homeomorphic to that of a stable map of 5 \ We also deduce a Morse-type inequality for s...

Elimination of singularities of smooth mappings of 4-manifolds into 3-manifolds

The simplest singularities of smooth mappings are fold singularities. We say that a mapping f is a fold mapping if every singular point of f is of the fold type. We prove 1 that for a closed orientable 4-manifold M4 the following conditions are equivalent: (1) M4 admits a fold mapping into R3; (2) for every orientable 3-manifold N3, every homotopy class of mappings of M4 into N3 contains a fold...

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

On the Linear Combinations of Slanted Half-Plane Harmonic Mappings

‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

Stable Exponentially Harmonic Maps Between Finsler Manifolds