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Journal of the London Mathematical Society 1976 s2-14(2):357-363; doi:10.1112/jlms/s2-14.2.357
© 1976 by London Mathematical Society
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© Oxford University Press

Ein Produktsatz Für Die Zweite Totalkrümmung

Wolfgang Kühnel

Technische Universität Berlin (Fachbereich 3) Berlin, Germany

It is a well-known theorem proved by Willmore and Saleemi (cf. [5]) that the total absolute curvature of a product-immersion equals the product of the total absolute curvatures of the factors. In this note we consider the same situation for the second total curvature of order 2 and prove a similar product theorem. In case of the product of two surfaces we get inequalities similar to that of Chern and Lashof (cf. [2]).


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