- 3-spaces).{{cite book}}: CS1 maint:
postscript (link) Barnea, Nir (1999). "
Hyperspherical functions with
arbitrary permutational symmetry:
Reverse construction"...
-
antipodal points in
elliptic geometry. For example, this is
achieved in the
hyperspherical model (described below) by
making the "points" in our
geometry actually...
- ellipsoid. Generally, the n {\displaystyle n} -dimensional
volume of a
hyperspherical cap of
height h {\displaystyle h} and
radius r {\displaystyle r} in...
-
coordinates are
given below. It is
convenient to have some sort of
hyperspherical coordinates on S3 in
analogy to the
usual spherical coordinates on S2...
-
rewrite it in
hyperspherical coordinates, we can use the
decomposition of a
plane wave into d {\textstyle d} -dimensional
hyperspherical harmonics Y l...
- is elliptical, i.e. a 3-sphere with
opposite points identified.) In
hyperspherical or curvature-normalized
coordinates the
coordinate r is proportional...
-
universe is
hyperspherical and Rt is the
radius of
curvature (R0 at the present), then a = Rt/R0. If k is positive, then the
universe is
hyperspherical. If k...
-
matrix coefficients of the m {\displaystyle m} th
representation are
hyperspherical harmonics of
degree m {\displaystyle m} , that is, the restrictions...
-
position coordinates to lie
inside the box, and the
momenta to lie on a
hyperspherical surface in
momentum coordinates of
radius U. If on the
other hand, the...
-
extended to higher-dimensional spaces, and is then
referred to as a
hyperspherical coordinate system. To
define a
spherical coordinate system, one must...
