Surfaces with maximal Lipschitz-Killing curvature in the direction of mean curvature vector

Author:
Chorng-shi Houh

Journal:
Proc. Amer. Math. Soc. **35** (1972), 537-542

MSC:
Primary 53A05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0301645-2

MathSciNet review:
0301645

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Abstract | References | Similar Articles | Additional Information

Abstract: is an oriented surface in . If is pseudo-umbilical, the Lipschitz-Killing curvature takes maximum in the direction of mean curvature vector. The converse is also investigated. Furthermore assuming that is closed, pseudo-umbilical and its Gaussian curvature has some nonnegative lower bound, is completely determined by the *M*-index of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0301645-2

Keywords:
Lipschitz-Killing curvature,
mean curvature vector,
*M*-index,
normal curvature,
pseudo-umbilical,
scalar normal curvature

Article copyright:
© Copyright 1972
American Mathematical Society