The Linearized System for Isometric Embeddings and Its Characteristic Variety

Details The Linearized System for Isometric Embeddings and Its Characteristic Variety The Linearized System for Isometric Embeddings and Its Characteristic Variety

2011-11-21

arxiv.org/abs/1111.4722v1

Mathematics

Differential Geometry

Advances in Mathematics, to appear, 29 pages

Scientific paper

In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension greater than 4. This is accomplished by introducing a smaller yet equivalent linearized system, in an appropriate way, which facilitates analysis of the characteristic variety.

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