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The Curvatures of Some Skew Fundamental Forms

1977
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Proceedings of the American Mathematical Society
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Fix a unit normal vector field on a surface C4-immersed in a Riemannian 3-manifold of constant sectional curvature. Suppose H and K are mean and Gauss curvatures respectively, and that H' = V/72 -K. Wherever H' •> 0, define I', II' and III' by HI = II -HI, H'W = H\\ -K\ and III' = Hit -XT, where I and II are the first and second fundamental forms. For constants a, ß, and v, let A' = at + ßlt + yïlt. Wherever H' ¥= 0 and A' is nondegenerate, the curvature of this (not necessarily Riemannian)

doi:10.2307/2041037
fatcat:yvzjfc6xkbbavl757btdw3s4k4