The 24 symmetry pairings of self-dual maps on the sphere

Local Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure

We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...

Enumeration of self-dual planar maps

A planar map is an embedding of a connected planar graph in the sphere such that the surface is partitioned into simply connected regions; in other words, it is a finite cellular decomposition of the sphere into vertices, edges, and faces (0−, 1− and 2−cells, respectively). In particular, 3−connected planar maps correspond to polyhedra. Motivated by the Four Colour Problem, W. Tutte [4] launche...

Dual multiwavelet frames with symmetry from two-direction renable functions

The second dual of strongly zero-product preserving maps

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...

Self-dual maps on the sphere

We show how to recursively construct all self–dual maps on the sphere together with their self–dualities, and classify them according to their edge–permutations. Although several well known classes of self–dual graphs, e.g., the wheels, have been known since the last century, [7], the general characteristics of self–dual graphs have only recently begun to be explored. In [10] two constructions ...