No abstract

A tiling of the Euclidean plane, by regular polygons, is called 2-uniform tiling if it has two orbits of vertices under the action of its symmetry group. There are 20 distinct 2-uniform tilings of the plane. Plane being the universal cover of torus and Klein bottle, it is natural to ask about the exploration of maps on these two surfaces corresponding to the 2-uniform tilings. We call such maps as doubly semiequivelar maps. In the present study, we compute and classify (up to isomorphism) doubly semiequivelar maps on torus and Klein bottle. This classification of semiequivelar maps is useful in classifying a category of symmetrical maps which have two orbits of vertices, named as 2-uniform maps.

In this paper, the non-existence of connected, compact Einstein doubly warped product semi-Riemannian manifold with non-positive scalar curvature is proved. It is also shown that there does not exist non-trivial connected Einstein doubly warped product semi-Riemannian manifold with compact base $B$ or fibre $F$.

We find the index of∇˜-quasiconformally symmetric and∇˜-concircularly symmetric semi-Riemannian manifolds, where∇˜is metric connection.

Our results suggest that a selective approach may be exercised in the use of transesophageal echocardiography prior to D.C. cardioversion for atrial fibrillation. Patients with an entirely "normal" transthoracic echocardiogram may proceed directly to cardioversion without a precardioversion transesophageal echocardiogram.