|
|
|
|
| LEADER |
03639cam a2200361uu 4500 |
| 001 |
820840d1-0252-4bf3-8fc7-853730eee3f5 |
| 003 |
miami |
| 005 |
20160805 |
| 007 |
c||||||||||||a| |
| 008 |
160805e20160805||||||||||#s||||||||eng|||||| |
| 024 |
7 |
|
|a urn:nbn:de:hbz:6-45219527483
|2 urn
|
| 041 |
|
|
|a eng
|
| 082 |
0 |
|
|a 510 Mathematik
|2 23
|
| 100 |
1 |
|
|a Jäger, Florian
|0 http://d-nb.info/gnd/1109808852
|4 aut
|
| 110 |
2 |
|
|a Universitäts- und Landesbibliothek Münster
|0 http://d-nb.info/gnd/5091030-9
|4 own
|
| 245 |
1 |
0 |
|a An algebraic characterization of the Weyl curvature of Sm × Sm
|
| 246 |
1 |
3 |
|a An algebraic characterization of the Weyl curvature of S m × S m
|
| 250 |
|
|
|a [Electronic ed.]
|
| 264 |
|
1 |
|c 2016
|
| 264 |
|
2 |
|b Universitäts- und Landesbibliothek Münster
|c 2016-08-05
|
| 505 |
0 |
|
|a Introduction 1 -- 1 Preliminaries 7 -- 1.1 The Ricci flow and the evolution of curvature operators . . . 7 -- 1.2 Algebraic curvature operators . . . . . . . . . . . . . . . . . . 8 -- 1.3 The #-map and its properties . . . . . . . . . . . . . . . . . . 9 -- 1.4 Diagonal algebraic curvature operators . . . . . . . . . . . . . 11 -- 2 Some new examples 15 -- 2.1 Legendre symbols and circulant matrices . . . . . . . . . . . . 16 -- 2.2 Infinite series of new solutions to W2 +W# = θW . . . . . . 20 -- 2.3 The isotropy groups of the new solutions . . . . . . . . . . . . 27 -- 3 Proof of theorem A 33 -- 3.1 The Weyl curvature of Sm × Sm . . . . . . . . . . . . . . . . 35 -- 3.2 A gap phenomenon for the scalar curvature . . . . . . . . . . 37 -- 3.3 Estimates for r2, scal, tr Ric3, and tr Ric4 . . . . . . . . . . . 42 -- 3.4 An estimate for −2⟨Ric(W2−), Ric⟩ . . . . . . . . . . . . . . . 48 -- 3.4.1 An estimate for T1 . . . . . . . . . . . . . . . . . . . . 49 -- 3.4.2 An estimate for T2 . . . . . . . . . . . . . . . . . . . . 54 -- 3.5 The scalar curvature cannot be too small . . . . . . . . . . . 64 -- 3.6 Conclusion: W is the normalized Wely curvature of Sm × Sm 75.
|
| 506 |
0 |
|
|a free access
|
| 520 |
3 |
|
|a In der vorliegenden Arbeit wird die Eigenwertgleichung W2+W#=θW, die in enger Beziehung zur Evolutionsgleichung von Krümmungsoperatoren unter dem Ricci Fluss steht, für Weyl Krümmungsoperatoren W untersucht. Es wird bewiesen, dass θ unter gewissen Bedingungen genau dann maximal ist, falls W die Weyl Krümmung von Sm×Sm ist. Desweitern werden unendliche Serien von neuen Lösungen dieser Eigenwertgleichung konstruiert.
|
| 520 |
3 |
|
|a In the present work, the eigenvalue equation W2+W#=θW, which is closely related to the evolution equation of a curvature operator under the Ricci flow, is analyzed for Weyl curvature operators W. A proof that under certain conditions θ is maximal if and only if W is the Weyl curvature of Sm×Sm is given. Moreover, infinite series of new solutions to this eigenvalue equation are constructed.
|
| 521 |
|
|
|a specialized
|
| 540 |
|
|
|a InC 1.0
|u https://rightsstatements.org/vocab/InC/1.0/
|
| 653 |
|
0 |
|a Ricci Fluss
|a Evolutionsgleichung
|a Krümmungsoperator
|a Weyl Krümmung
|a Eigenwertgleichung
|a Legendre Symbol
|
| 653 |
|
0 |
|a Ricci flow
|a evolution equation
|a curvature operator
|a Weyl curvature
|a eigenvalue equation
|a Legendre symbol
|
| 655 |
|
7 |
|2 DRIVER Types
|a Dissertation/Habilitation
|
| 655 |
|
7 |
|2 DCMI Types
|a Text
|
| 700 |
1 |
|
|a Böhm, Christoph
|u FB 10: Mathematik und Informatik
|4 ths
|
| 856 |
4 |
0 |
|3 Zum Volltext
|q text/html
|u https://nbn-resolving.de/urn:nbn:de:hbz:6-45219527483
|u urn:nbn:de:hbz:6-45219527483
|
| 856 |
4 |
0 |
|3 Zum Volltext
|q application/pdf
|u https://repositorium.uni-muenster.de/document/miami/820840d1-0252-4bf3-8fc7-853730eee3f5/diss_jaeger_florian.pdf
|
