منابع مشابه
FIXED POINTS OF ROTATIONS OF n-SPHERE
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Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least one fixed point in the interior of the ball. We generalize Schirmer’s result by proving that a smooth self-map of Euclidean n-space that extends a self-map of the unit sphere of that clas...
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The set Rot(S) of such rotations forms a group, most naturally viewed as a subgroup of GL3(R). Showing this requires some linear algebra. Recall that if m ∈ M3(R), meaning that m is a 3-by-3 real matrix, then its transpose m is obtained by flipping about the diagonal. That is, mij = mji for i, j = 1, 2, 3. The transpose is characterized by the more convenient condition 〈mx, y〉 = 〈x,my〉 for all ...
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We describe decomposition formulas for rotations of R 3 and R 4 that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in S 2 R 3. This analysis provides a pattern for our analysis of stereographic projections of the Cliiord torus C S 3 R 4. We use the higher dimensional decompositio...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1999
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171299222211