 About 3,380 results  books.google.com Spacelike Surfaces in PseudoEuclidean Space 10.1. The PseudoSphere
Consider the 3dimensional pseudoEuclidean space U\, with coordinates (t, x, y
) in terms of which the pseudoEuclidean metric has the form dl2 = dt2  dx2  dy2. 

 books.google.com The pseudodifferential calculus presented here has an elementary character, being addressed to a large audience of scientists. It includes the standard classes with global homogeneous structures, the socalled G and Γ operators  

 books.google.com The solutions might be to design a mapping into pseudoEuclidean space. ... The
results also hold for Euclidean cases, i.e. when the Gram operator derived from
distances is positive definite, and co incide with the classical scaling [7,8]. 

 books.google.com The difference between these two interpretations depends on how the time co
Figure 11.9 Hermann Minkowski 18641909 introduced ... Euclidean space : (x, y,
z, ct) pseudo  Euclidean space : (x, y, z, ict) The multiplying factor c converts time
... 

 books.google.com In particular, for the Blaschke quasielliptic space Sl'3 , the absolute consists of a
pair of imaginary conjugate planes, their intersection ... (The Blaschke metric in
the group of motions of the plane R2 is defined as follows: the distance co
between two motions A and B is ... space S121] whose particular cases _ __1 . n
"'0 1n the absom0 , ml ,n ,n—1,n are the pseudoEuclidean space R7 and its dual
space ... 

 books.google.com Dmitri♯Ư Vladimirovich Alekseevski♯Ư, Helga Baum  2008  Preview To be full is not really a restriction for submanifolds M of the Euclidean space R"
since we may always consider the smallest affine ... there are many submanifolds
of the pseudoEuclidean space Rp'q that are contained in an affine subspace that
is degenerate with respect to ... T^M. This implies that sx 6 O(p,q) for all x e M. We
define the transvection group of M C Rp'q by K := (sx o sy  x,y e M ) C O(p, q). 

 books.google.com Clearly p C O(F), so by construction (p(x) = x' . The case of a hyperboloid X is
similar. The only difference is that the inner product determined by the
polarization of q makes V into a pseudo Euclidean space of signature (k, 1), k + l
= n. Here the ... 

 books.google.com ... position vector can be decomposed into a finite sum of vector eigenfunctions of
the Laplacian of N: x:cO+x1+~~~+x;,, (7.8) where ... For integers k Z 1 and s Z 0,
every null ktype spacelike submanifold of the pseudo Euclidean mspace IE1? 

 books.google.com Next we want to express the Mobius invariants of a circle pair (Co, ... If 01, 02 and
bi, &2 are orthonormal bases for the Euclidean subspaces W ,U of the pseudo
Euclidean vector space V5 determining the circles Co, Ci, then the coordinates of
... 

 books.google.com Thus we get a Smarandachely embedded graph GR" in the pseudoEuclidean
space (R", ,u) by Theorem 8.4.4. ... if U I W or a bounded metric pseudospace if
there is a number N > 0 such that Vw G W, p(w) S N, denoted by (U, to) or (U _, co
), ... 

 