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

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- by Chorng-shi Houh
- Proc. Amer. Math. Soc.
**35**(1972), 537-542 - DOI: https://doi.org/10.1090/S0002-9939-1972-0301645-2
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## Abstract:

${M^2}$ is an oriented surface in ${E^{2 + N}}$. If ${M^2}$ is pseudo-umbilical, the Lipschitz-Killing curvature takes maximum in the direction of mean curvature vector. The converse is also investigated. Furthermore assuming that ${M^2}$ is closed, pseudo-umbilical and its Gaussian curvature has some nonnegative lower bound, ${M^2}$ is completely determined by the*M*-index of ${M^2}$.

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## Bibliographic Information

- © Copyright 1972 American Mathematical Society
- 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