Planar geodesic immersions

Geodesic Embeddings and Planar Graphs

Manhattan-Geodesic Embedding of Planar Graphs

In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains of axis-parallel line segments, that is, as geodesics with respect to the Manhattan metric. First, we show that geodesic embeddability on the grid is equivalent to 1-bend embeddability on the grid. For the latter quest...

Visual Contours and Planar Sections for Affine Immersions

In this paper we consider planar sections and visual contours of co-dimension one affine immersions. The main theorem says that the third order Taylor expansion of the difference between the visual contour and planar section functions is exactly the cubic form. We also consider parameterizations on two dimensional affine immersions whose coordinate lines are geodesics, in one direction, and bot...

Totally geodesic Kähler immersions in view of curves of order two

In this paper, we characterize of totally geodesic Kähler immersions by extrinsic shapes of some curves having points of order 2.

Closures of Totally Geodesic Immersions in Manifolds of Constant Negative Curvature

Let 800(1, n) denote the connected component of the group of linear transformations of IRn+l preserving the bilinear form Abstract Using techniques of Lie groups and ergodic theory, it can be shown that in a compact manifold of constant negative curvature, the closure of a totally geodesic, complete (immersed) submanifold of dimension atleast 2 is a totally geodesicimmersed submanifold. The mai...