The Nature of Elliptic Sectors in the Principal Foliations of Surface Theory
نویسنده
چکیده
Little is known of the geometry of the principal foliations on a smooth surface in R3. The unsolved Carathéodory conjecture for such a surface would follow from Bendixson’s formula for the index of an isolated singularity of a smooth foliation on a smooth 2-manifold, were it known that on a smooth surface the principal foliations never admit an elliptic sector at an isolated umbilic. Evidence in favour of the nonexistence of such elliptic sectors in principal foliations is the main result here and offers a first geometric explanation of why the conjecture might be true for smooth surfaces. §
منابع مشابه
Non-existence of Elliptic Sectors in the Principal Foliations of Surface Theory
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تاریخ انتشار 2004