Type
Text
Type
Dissertation
Advisor
KHURI, MARCUS | MICHAEL ANDERSON | DARYL GELLER | CHRISTINA SORMANI.
Date
2010-08-01
Keywords
Mathematics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/72636
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We prove the following result: Let $(M,g)$ be a 3-dimensional $C^\infty$ Riemannian manifold for which there exists a $p\in M$ and a $v\in T_pM$ such that$$ \mathbf{Riem}(p) = 0 \ \ \ \ \ \text{and} \ \ \ \ \ \nabla_v\mathbf{Riem}(p) \neq 0. $$ Then there exists a $C^\infty$ local isometric embedding from a neighbourhood of $p$ into $\mathbb{R}^6$.
Recommended Citation
Poole, Thomas Edward, "The local isometric embedding problem for 3-dimensional Riemannian manifolds with cleanly vanishing curvature" (2010). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 1839.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/1839