Difference between revisions of "Elliptic point"
From Encyclopedia of Mathematics
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A point on a regular surface at which the osculating paraboloid is an elliptic paraboloid. In an elliptic point the Dupin indicatrix is an ellipse, the Gaussian curvature of the surface is positive, the principal curvatures of the surface are of the same sign, and for the coefficients of the second fundamental form of the surface the inequality | A point on a regular surface at which the osculating paraboloid is an elliptic paraboloid. In an elliptic point the Dupin indicatrix is an ellipse, the Gaussian curvature of the surface is positive, the principal curvatures of the surface are of the same sign, and for the coefficients of the second fundamental form of the surface the inequality | ||
| − | + | $$LN-M^2>0$$ | |
holds. In a neighbourhood of an elliptic point the surface is locally convex. | holds. In a neighbourhood of an elliptic point the surface is locally convex. | ||
Latest revision as of 19:12, 12 April 2014
A point on a regular surface at which the osculating paraboloid is an elliptic paraboloid. In an elliptic point the Dupin indicatrix is an ellipse, the Gaussian curvature of the surface is positive, the principal curvatures of the surface are of the same sign, and for the coefficients of the second fundamental form of the surface the inequality
$$LN-M^2>0$$
holds. In a neighbourhood of an elliptic point the surface is locally convex.
How to Cite This Entry:
Elliptic point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elliptic_point&oldid=31652
Elliptic point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elliptic_point&oldid=31652
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article