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Isometric embedding via strongly symmetr...
Chen, Gui-Qiang...

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Isometric embedding via strongly symmetric positive systems by Chen, Gui-Qiang ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated arguments via microlocal analysis used in earlier proofs. In Part 1, we introduce a new type of system of partial differential equations, which is not one of the standard types (elliptic, hyperbolic, parabolic) but satisfies a property called strong symmetric positivity. Such a PDE system is a generalization of and has properties similar to a system of ordinary differential equations with a regular singular point. A local existence theorem is then established by using a novel local-to-global-to-local approach. In Part 2, we apply this theorem to prove the local existence result for isometric embeddings.
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Article
pdf
29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.04356
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