On geodesic triangles with right angles in a dually flat space
share
The dualistic structure of statistical manifolds yields eight types of geodesic triangles defining overall eighteen interior angles. In general, the interior angles of geodesic triangles can sum up to π like in Euclidean/Mahalanobis geometry, or exhibit either angle excesses or angle defects. In this paper, we initiate the study of geodesic triangles in dually flat spaces where a generalized Pythagorean theorem holds. First, we show when it is possible how to construct geodesic triangles which either have one, two, or three interior right angles. Then we report a construction of triples of points for which the dual Pythagorean theorems hold simultaneously at a point, yielding two dual pairs of dual geodesic triangles with doubly right angles.
READ FULL TEXT
