Intrinsic and Extrinsic Geometry of Ovaloids and Rigidity

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Author(s) : Udo Simon, Luc Vrancken, Changping Wang, Martin Wiehe

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 687-2000

MSC 2000

53C42 Immersions
53C24 Rigidity results

Abstract :
Our main result is that an ovaloid with nowhere dense umbilics and prescribed Weingarten operator and spherical volume form is rigid in Euclidean 3-space. In case of an ovaloid of revolution we can drop the assumption on the volume form.

Keywords : ovaloids, global rigidity, Weingarten operator, surfaces of revolution

Notes :
Published in: Geometry and Topology of Submanifolds X, W.H. Chen et al. (eds), World Scientific, Singapore, 284-293 (2000).