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- W2770617770 abstract "In this paper, we investigate the behavior of the curvature of nondevelopable surfaces around an umbilic point at the origin. The surfaces are of the form z = f(x, y) where f is a nonhomogeneous bivariate polynomial with cubic and quartic terms. We do this by looking at the continuity of the principal directions around the origin as well as the rate that the principal curvatures converge to zero as they approach the origin. This is done by considering the eigenvectors and eigenvalues of the shape operator. In our main result, we prove that a continuously diagonalizable shape operator implies the existence of a path through the origin with noncomparable principal curvatures. Acknowledgements: I would like to thank my research mentor, Dr. Phillip Harrington, for his assistance with this work. I owe much of my success to his teachings and guidance. I would also like to thank Weston Barger and William Lewis for all of their encouragement during my years as an undergraduate. Page 76 RHIT Undergrad. Math. J., Vol. 15, No. 2" @default.
- W2770617770 created "2017-12-04" @default.
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- W2770617770 date "2014-01-01" @default.
- W2770617770 modified "2023-09-26" @default.
- W2770617770 title "Continuously Diagonalizing the Shape Operator" @default.
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