Search results
Results from the WOW.Com Content Network
which vanishes if and only if Γ i kj is symmetric on its lower indices. Given a metric connection with torsion, one can always find a single, unique connection that is torsion-free, this is the Levi-Civita connection. The difference between a Riemannian connection and its associated Levi-Civita connection is the contorsion tensor.
Local connectedness is, by definition, a local property of topological spaces, i.e., a topological property P such that a space X possesses property P if and only if each point x in X admits a neighborhood base of sets that have property P. Accordingly, all the "metaproperties" held by a local property hold for local connectedness. In particular:
Alternatively, a might have a direct reference to object c and make the request directly to that. If the law is followed, only object b knows its own internal structure. More formally, the Law of Demeter for functions requires that a method m of an object a may only invoke the methods of the following kinds of objects: [5] a itself; m's parameters;
Most of the algebraic properties of the Christoffel symbols follow from their relationship to the affine connection; only a few follow from the fact that the structure group is the orthogonal group O(m, n) (or the Lorentz group O(3, 1) for general relativity). Christoffel symbols are used for performing practical calculations.
The connection on the frame bundle can also be described using K-invariant differential 1-forms on F. [7] [34] The orthonormal frame bundle F is a 3-manifold. One of the key facts about F is that it is (absolutely or completely) parallelizable, i.e. for n = dim F, there are n vector fields on F which form a basis at each point.
In mathematics, a local system (or a system of local coefficients) on a topological space X is a tool from algebraic topology which interpolates between cohomology with coefficients in a fixed abelian group A, and general sheaf cohomology in which coefficients vary from point to point.
You can find instant answers on our AOL Mail help page. Should you need additional assistance we have experts available around the clock at 800-730-2563.
An adequately defined interface will allow one team to test its implementation of the interface by simulating the opposing side with a simple communications simulator. Not knowing the business logic of the system on the far side of an interface makes it more likely that one will develop a system that does not break when the other system changes ...