Author： Ando N.
Publisher： Springer Publishing Company
ISSN： 0046-5755
Source： Geometriae Dedicata, Vol.82, Iss.1-3, 2000-10, pp. : 115-137
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Abstract
Suppose that the origin o of R^3 is an isolated umbilical point of the graph of a homogeneous polynomial in two real variables of degree k3. Then we see that the index of o is an element of the set 1-k/2+i^[k/2]_i=0. Moreover, we see that each element of 1-k/2+i^[k/2]_i=0 may be the index of o on the graph of a suitable homogeneous polynomial of degree k.
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