Learn more about our help with Assignments: Topology
Search
Differential Geometry | Topology
Calculate the principal, Gaussian, and mean curvatures of the surface of revolution
σ(u, v) = (f(u) cos v, f(u) sin v, g(u)), where f, g are smooth real-valued functions
with f > 0.
σ(u, v) = (f(u) cos v, f(u) sin v, g(u)), where f, g are smooth real-valued functions
with f > 0.
Differential Geometry | Topology
Calculate the normal and the geodesic curvatures of the following curves on
the given surfaces:
(a) The circle γ(t) = (cost, sin t, 1) on the paraboloid σ(u, v) = (u, v, u^2 + v^2).
(b) The right circular helix γ(θ) = (a cos θ, a sin θ, bθ) on the right circular cylinder
σ(u, v) = (a cos u, a sin u, v), where a, b > 0 are constants.
the given surfaces:
(a) The circle γ(t) = (cost, sin t, 1) on the paraboloid σ(u, v) = (u, v, u^2 + v^2).
(b) The right circular helix γ(θ) = (a cos θ, a sin θ, bθ) on the right circular cylinder
σ(u, v) = (a cos u, a sin u, v), where a, b > 0 are constants.
Differential Geometry | Topology
Calculate the first fundamental form, the second fundamental form, and the
Weingarten matrix of the following surface patches of the unit sphere:
(a) σ(θ, φ) = (cos θ cos φ, cos θ sin φ,sin θ).
(b) σ(u, v) = (sech u cos v, sech u sin v, tanh u).
Weingarten matrix of the following surface patches of the unit sphere:
(a) σ(θ, φ) = (cos θ cos φ, cos θ sin φ,sin θ).
(b) σ(u, v) = (sech u cos v, sech u sin v, tanh u).
Differential Geometry | Topology
A set S is cardinally majorizable by a set T iff there exists a(n) ______________ from T to S.
It is not injection. Bijection from T to S? Maybe so that there will be injection from S to T.
Differential Geometry | Topology
Q5 Let F be closed set. Prove that ∀ A subset and equel to X；line over (F∩A)subset and equel to (F∩(lin overA)).
Differential Geometry | Topology
Q/in cofinite topology (X,C), P∈X, Show that N(p) subset and equel to C were N(p) is set of all neignborhoods of p.
Differential Geometry | Topology
Q/ The union of infinite collcction of closed set may not be closcd. Give an example
Differential Geometry | Topology
Q/State all possible topologies on set X ={1,2,3, 4}.
Differential Geometry | Topology
Q/Let T be the class of subsets of N consisting of empty set and all subscts of the form Gn ={n,n +1,n+ 2,..} with n € N. Show that T is topology on N.
Differential Geometry | Topology
Find the equation of the tangent plane of the following surface patches
at the indicated points:
(b) σ(r, θ) = (r cos θ, r sin θ, 2θ), P =
√
3, 1,
π
3
at the indicated points:
(b) σ(r, θ) = (r cos θ, r sin θ, 2θ), P =
√
3, 1,
π
3
