| LDR | | 00000nam u2200205 4500 |
| 001 | | 000000433286 |
| 005 | | 20200225133258 |
| 008 | | 200131s2019 ||||||||||||||||| ||eng d |
| 020 | |
▼a 9781085623469 |
| 035 | |
▼a (MiAaPQ)AAI13865898 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 247004 |
| 082 | 0 |
▼a 510 |
| 100 | 1 |
▼a Krishnan, Anusha Mangala. |
| 245 | 10 |
▼a Ricci Flow on Cohomogeneity One Manifolds. |
| 260 | |
▼a [S.l.]:
▼b University of Pennsylvania.,
▼c 2019. |
| 260 | 1 |
▼a Ann Arbor:
▼b ProQuest Dissertations & Theses,
▼c 2019. |
| 300 | |
▼a 83 p. |
| 500 | |
▼a Source: Dissertations Abstracts International, Volume: 81-03, Section: B. |
| 500 | |
▼a Advisor: Ziller, Wolfgang. |
| 502 | 1 |
▼a Thesis (Ph.D.)--University of Pennsylvania, 2019. |
| 506 | |
▼a This item must not be sold to any third party vendors. |
| 520 | |
▼a 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. |
| 590 | |
▼a School code: 0175. |
| 650 | 4 |
▼a Mathematics. |
| 690 | |
▼a 0405 |
| 710 | 20 |
▼a University of Pennsylvania.
▼b Mathematics. |
| 773 | 0 |
▼t Dissertations Abstracts International
▼g 81-03B. |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0175 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2019 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T15491059
▼n KERIS
▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
| 980 | |
▼a 202002
▼f 2020 |
| 990 | |
▼a ***1816162 |
| 991 | |
▼a E-BOOK |