Relation To Differential Geometry
On a manifold, locally we may assign a tangent surface spanned by a set of basis vectors . We can associate the components of a metric tensor, the Christoffel symbols, and the Riemann tensor as follows:
These relations embed the theory of differential geometry within geometric calculus.
Read more about this topic: Geometric Calculus
Famous quotes containing the words relation to, relation, differential and/or geometry:
“Light is meaningful only in relation to darkness, and truth presupposes error. It is these mingled opposites which people our life, which make it pungent, intoxicating. We only exist in terms of this conflict, in the zone where black and white clash.”
—Louis Aragon (1897–1982)
“The difference between objective and subjective extension is one of relation to a context solely.”
—William James (1842–1910)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“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)