Parallel Transport in Riemannian Geometry
In (pseudo) Riemannian geometry, a metric connection is any connection whose parallel transport mappings preserve the metric tensor. Thus a metric connection is any connection Γ such that, for any two vectors X, Y ∈ Tγ(s)
Taking the derivative at t=0, the associated differential operator ∇ must satisfy a product rule with respect to the metric:
Read more about this topic: Parallel Transport
Famous quotes containing the words parallel, transport and/or geometry:
“The parallel between antifeminism and race prejudice is striking. The same underlying motives appear to be at work, namely fear, jealousy, feelings of insecurity, fear of economic competition, guilt feelings, and the like. Many of the leaders of the feminist movement in the nineteenth-century United States clearly understood the similarity of the motives at work in antifeminism and race discrimination and associated themselves with the anti slavery movement.”
—Ashley Montagu (b. 1905)
“One may disavow and disclaim vices that surprise us, and whereto our passions transport us; but those which by long habits are rooted in a strong and ... powerful will are not subject to contradiction. Repentance is but a denying of our will, and an opposition of our fantasies.”
—Michel de Montaigne (1533–1592)
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)