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

Houh, Chorng-shi

doi:10.1090/S0002-9939-1972-0301645-2

Surfaces with maximal Lipschitz-Killing curvature in the direction of mean curvature vector
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Proc. Amer. Math. Soc. 35 (1972), 537-542 Request permission

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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