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Ricci Flow on Cohomogeneity One Manifolds
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Ricci Flow on Cohomogeneity One Manifolds. |
| 개인저자 | Krishnan, Anusha Mangala. |
| 단체저자명 | University of Pennsylvania. Mathematics. |
| 발행사항 | [S.l.]: University of Pennsylvania., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 83 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-03B. Dissertation Abstract International |
| ISBN | 9781085623469 |
| 학위논문주기 | Thesis (Ph.D.)--University of Pennsylvania, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Advisor: Ziller, Wolfgang. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | In the first part of this thesis, in joint work with Renato Bettiol, we show that the geometric property of nonnegative sectional curvature is not preserved under the Ricci flow on closed manifolds of dimension greater than or equal to 4. This is in contrast to the situation for 3 dimensional manifolds. The main strategy is to study the Ricci flow equation on certain 4 dimensional manifolds that admit an isometric group action of cohomogeneity one.Along the way we need to show that a certain canonical form for an invariant metric on a cohomogeneity one manifold, is preserved under the Ricci flow. In the particular situation of the above mentioned result, we prove the preservation of that canonical form using an ad hoc method. It is an interesting question whether this canonical form for a cohomogeneity one metric is preserved in general. In the second part of the thesis we present a strategy to tackle this problem, explain its geometric consequences, and also explain the challenges in carrying out the strategy, along with some partial results. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
