We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M, cM ) to a twodimensional conformal manifold (N, cN ) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H, g) of (M, cN ) to (N, cN ). Moreover, any positive harmonic morphism with two-dimensional fibres from (H, g) is obtained this way.

Let G = Z/ps ( p an odd prime). We show that restricting the local representations in a unitary G-manifold M with isolated fixed points results in severe restrictions on the number of fixed points (counted with the sign of their orientation), paralleling results obtained by Conner and Floyd in the case G = Z/p . Specifically, the number of noncancelling fixed points is either zero or divisible ...

Let M be a connected smooth G-manifold, where G is a connected compact Lie group. In this paper, we first study the relation between π1 (M) and π1 (M/G). Then we particularly focus on the case when M is a connected Hamiltonian G-manifold with an equivariant moment map φ. In [13], for compact M , we proved that π1 (M) = π1 (M/G) = π1 (Ma) for all a ∈ image(φ), where Ma is the symplectic quotient...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

It is known that every closed compact orientable 3-manifold M can be represented by a 4-edge-coloured 4-valent graph called a crystallisation of M. Casali and Grasselli proved that 3-manifolds of Heegaard genus g can be represented by crystallisations with a very simple structure which can be described by a 2(g +1)-tuple of non-negative integers. The sum of first g +1 integers is called complex...

Interest in group actions with the property that the orbit space has greater dimension than the original space is motivated in part by P. A. Smith’s generalization [S2] of Hilbert’s Fifth Problem [H]. Hilbert asked whether a topological group G the underlying space of which, |G|, is a (finitedimensional) manifold admits the structure of a Lie group, i.e., whether |G| admits the structure of a r...

Given a C∞ Riemannian metric g on RP 2 we prove that (RP , g) has constant curvature iff all geodesics are closed. Therefore RP 2 is the first non trivial example of a manifold such that the smooth Riemannian metrics which involve that all geodesics are closed are unique up to isometries and scaling. This remarkable phenomenon is not true on the 2-sphere, since there is a large set of C∞ metric...

This project aims to find correlations between various flow parameters and liquid refrigerant flow distribution within a horizontal manifold supplying two-phase R134a downward into fifteen aluminum microchannels. Liquid flow rates, system pressures, and refrigerant temperatures are recorded. Prior to this project, similar experiments were conducted using an identical manifold setup with water/a...

We expose the theory of the construction of a natural G 2 structure on the unit sphere tangent bundle SM of any given orientable Riemannian 4-manifold M , as laid in [4]. This time we work in the context of metric connections, or geometry with torsion. 1 Recalling the theory By a G 2 manifold it is understood a 7 dimensional Riemannian manifold with holonomy group contained in G 2 = Aut(O). The...