- (sometimes
called the
hedgehog theorem in Europe)
states that
there is no
nonvanishing continuous tangent vector field on even-dimensional n-spheres. For the...
- (1) by 0, −q, and μ respectively. Then the
constant function 1 is a
nonvanishing solution corresponding to the
eigenvalue μ0 = 0.
While there is no guarantee...
-
vacuum states. Its
hallmark under the
broken symmetry transformation is
nonvanishing vacuum expectation 〈δϕg〉, an
order parameter, for
vanishing 〈ϕg〉 = 0...
-
recognize the more
formal statement of the theorem, that
there is no
nonvanishing continuous tangent vector field on the sphere. As with the
Bridges of...
- 3-sphere
admits nonvanishing vector fields (sections of its
tangent bundle). One can even find
three linearly independent and
nonvanishing vector fields...
-
smooth manifolds, a
congruence is the set of
integral curves defined by a
nonvanishing vector field defined on the manifold.
Congruences are an
important concept...
- and the
density f of X. The ****umption that g is
differentiable with
nonvanishing derivative,
which is
necessary for
applying the
usual change-of-variables...
-
nonvanishing only for s ≤ x {\displaystyle s\leq x} ,
which is
called a ****ed Green's function, and
another Green's
function that is
nonvanishing only...
-
theory of
smooth manifolds, the set of
integral curves defined by a
nonvanishing vector field defined on the
manifold Congruence (general relativity)...
-
curvature tensor has
vanishing eigenvalues. A
Lorentzian manifold with
nonvanishing curvature is a (nontrivial) pp-wave if and only if it
admits a covariantly...
