Title

Constant Vector Curvature in Three Dimensions

Presenter Information

Albany Thompson

Document Type

Oral Presentation

Location

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.

Faculty Mentor(s)

James Bisgard

Department/Program

Mathematics

Additional Mentoring Department

Mathematics

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May 21st, 12:20 PM May 21st, 12:40 PM

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.