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The local isometric embedding problem for 3-dimensional Riemannian manifolds with cleanly vanishing curvature

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dc.contributor.advisor KHURI, MARCUS en_US
dc.contributor.author Poole, Thomas Edward en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2012-05-15T18:05:56Z
dc.date.available 2012-05-15T18:05:56Z
dc.date.issued 1-Aug-10 en_US
dc.date.submitted Aug-10 en_US
dc.identifier Poole_grad.sunysb_0771E_10185.pdf en_US
dc.identifier.uri http://hdl.handle.net/1951/55585
dc.description.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 $\mathbb{R}^6$. en_US
dc.description.sponsorship Stony Brook University Libraries. SBU Graduate School in Department of Mathematics. Lawrence Martin (Dean of Graduate School). en_US
dc.format Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.title The local isometric embedding problem for 3-dimensional Riemannian manifolds with cleanly vanishing curvature en_US
dc.type Dissertation en_US
dc.description.advisor Advisor(s): MARCUS KHURI. Committee Member(s): MICHAEL ANDERSON; DARYL GELLER; CHRISTINA SORMANI. en_US
dc.mimetype Application/PDF en_US


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