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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: $ {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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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