https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Parabolic_functionParabolic function - Revision history2026-10-19T16:25:54ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Parabolic_function&diff=1056&oldid=prevVipul: 1 revision2008-05-18T19:50:30Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://diffgeom.subwiki.org/w/index.php?title=Parabolic_function&diff=1055&oldid=prevVipul at 16:35, 5 April 20072007-04-05T16:35:22Z<p></p>
<p><b>New page</b></p><div>==Definition==<br />
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Let <math>(m_1,m_2,\ldots,m_r)</math> be a tuple of integers whose sum is <math>n</math>. Then, a function <math>f:\R^n \to \R^n</math> is said to be of parabolic type <math>(m_1,m_2,\ldots,m_r)</math> if for any <matH>k \le r</math>, the effect on the first <math>m_1 + m_2 \ldots m_k</math> coordinates is independent of the values of the remaining coordinates.<br />
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If <math>f</math> is also continuously differentiable, this is equivalent to the condition that the Jacobian matrix of <math>f</math> be of parabolic type <math>(m_!,m_2,\ldots,m_r)</math>.</div>Vipul