| LDR | | 00000nam u2200205 4500 |
| 001 | | 000000434399 |
| 005 | | 20200226150348 |
| 008 | | 200131s2019 ||||||||||||||||| ||eng d |
| 020 | |
▼a 9781392585627 |
| 035 | |
▼a (MiAaPQ)AAI22620071 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 247004 |
| 082 | 0 |
▼a 510 |
| 100 | 1 |
▼a Appleton, Alexander J. |
| 245 | 10 |
▼a Singularities in U(2)-Invariant 4d Ricci Flow. |
| 260 | |
▼a [S.l.]:
▼b University of California, Berkeley.,
▼c 2019. |
| 260 | 1 |
▼a Ann Arbor:
▼b ProQuest Dissertations & Theses,
▼c 2019. |
| 300 | |
▼a 178 p. |
| 500 | |
▼a Source: Dissertations Abstracts International, Volume: 81-06, Section: B. |
| 500 | |
▼a Advisor: Bamler, Richard |
| 502 | 1 |
▼a Thesis (Ph.D.)--University of California, Berkeley, 2019. |
| 506 | |
▼a This item must not be sold to any third party vendors. |
| 520 | |
▼a Firstly, we analyze the steady Ricci soliton equation for a certain class of metrics on complex line bundles over K\\"ahler-Einstein manifolds of positive scalar curvature. We show that these spaces admit a non-collapsed steady gradient Ricci soliton metric. In the four (real-) dimensional case, this yields a new family of non-collapsed steady Ricci solitons on the complex line bundles $O(-k)$, $k \\geq 3$, over $\\mathbb{C}P. |
| 520 | |
▼a 1$. These solitons are $U(2)$-invariant, non-K\\"ahler, and asymptotic to the the quotient of the four dimensional Bryant soliton by $\\Z_k$. As a byproduct of our work we also find Taub-Nut like Ricci solitons on $\\R. |
| 520 | |
▼a 4$ and demonstrate a new proof for the existence of the Bryant soliton.Secondly, we investigate the formation of singularities in four dimensional $U(2)$-invariant Ricci flow and show that the Eguchi-Hanson space can occur as a blow-up limit. In particular, we prove that starting from a class of asymptotically cylindrical $U(2)$-invariant initial metrics on $TS. |
| 520 | |
▼a 2$, a Type II singularity modeled on the Eguchi-Hanson space develops in finite time and the only possible blow-up limits are (i) the Eguchi-Hanson space, (ii) the flat $\\R. |
| 520 | |
▼a 4 / \\Z_2$ orbifold, (iii) the 4d Bryant soliton quotiented by $\\Z_2$, and (iv) the shrinking cylinder $\\R \imes \\R P. |
| 520 | |
▼a 3$. It also follows from our work that in four dimensional Ricci flow an embedded two dimensional sphere of any self-intersection number $k \\in \\Z$ may collapse to a point in finite time and thereby produce a singularity. For $|k|\\geq 3$ the singularities we construct are of Type II, yielding a new infinite family of Type II singularities. Numerical simulations indicate that their blow-up limits are the four dimensional steady Ricci solitons described above. |
| 590 | |
▼a School code: 0028. |
| 650 | 4 |
▼a Mathematics. |
| 690 | |
▼a 0405 |
| 710 | 20 |
▼a University of California, Berkeley.
▼b Mathematics. |
| 773 | 0 |
▼t Dissertations Abstracts International
▼g 81-06B. |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0028 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2019 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T15493683
▼n KERIS
▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
| 980 | |
▼a 202002
▼f 2020 |
| 990 | |
▼a ***1008102 |
| 991 | |
▼a E-BOOK |