Lobachevskian geometry, also known as hyperbolic geometry, is a non-Euclidean geometry that arises when the parallel postulate of Euclidean geometry is replaced with the notion that through any point not on a given line, there are at least two distinct lines that do not intersect the given line. This geometry is characterized by a consistent set of axioms where the sum of angles in a triangle is less than 180 degrees, and it models a space of constant negative curvature.