Disformal transformation in Newton–Cartan geometry

Disformal Inflation

We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms. This field drives inflation solely by its derivatives, which couple to the matter only through the combination ḡμν = gμν − 1 m4∂μφ∂νφ. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as φ̇ > m, and terminates gracefully once ...

Lie Transformation Groups and Geometry

We present geometrical aspects of Lie groups and reductive homogeneous spaces, and some resent results on homogeneous geodesics and homogeneous Einstein metrics. The article is based on the four lectures given in Varna, June 2007.

Transformation Optics and the Geometry of Light

On Geometry and Transformation in Map-Like Information Visualization

A number of visualization techniques have been put forward that implement a map metaphor to display abstract, non-georeferenced information. This paper refers to these as map-like information visualizations that are distinguished from other information visualization approaches in a number of ways. It interprets some of the principles underlying these techniques within a framework informed by ge...

Using dynamic geometry software to improve eight grade students’ understanding of transformation geometry

This study examines the effect of dynamic geometry software (DGS) on students’ learning of transformation geometry. A preand post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the transformation geometry in a (DGE), the same instructi...