# Constant Vector Curvature in Three Dimensions

## Document Type

Oral Presentation

## Campus where you would like to present

SURC 201

## Start Date

21-5-2015

## End Date

21-5-2015

## Keywords

Geometry, Curvature, Vectors

## Abstract

Differential geometry is the use of the techniques and tools of calculus to study the geometric properties of manifolds. One of the most commonly studied properties of manifolds is their curvature. We can measure the curvature of a manifold at a point by using a metric called an algebraic curvature tensor and a geometric object known as a model space. A model space is formed when a manifold, inner product, and algebraic curvature tensor are grouped together. There are several curvature conditions that a model space can satisfy. This research is concerned with the necessary and sufficient conditions for a model space in three dimensions with positive definite inner product to have the specific curvature condition of constant vector curvature. This presentation summarizes the background for this research along with its findings.

## Recommended Citation

Thompson, Albany, "Constant Vector Curvature in Three Dimensions" (2015). *Symposium Of University Research and Creative Expression (SOURCE)*. 44.

https://digitalcommons.cwu.edu/source/2015/oralpresentations/44

## Department/Program

Mathematics

## Additional Mentoring Department

Mathematics

Constant Vector Curvature in Three Dimensions

SURC 201

Differential geometry is the use of the techniques and tools of calculus to study the geometric properties of manifolds. One of the most commonly studied properties of manifolds is their curvature. We can measure the curvature of a manifold at a point by using a metric called an algebraic curvature tensor and a geometric object known as a model space. A model space is formed when a manifold, inner product, and algebraic curvature tensor are grouped together. There are several curvature conditions that a model space can satisfy. This research is concerned with the necessary and sufficient conditions for a model space in three dimensions with positive definite inner product to have the specific curvature condition of constant vector curvature. This presentation summarizes the background for this research along with its findings.

## Faculty Mentor(s)

James Bisgard