Volume 15, issue 2 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups

Michael Jablonski

Geometry & Topology 15 (2011) 735–764
Bibliography
1 D V Alekseevskiĭ, B N Kimel’fel’d, Structure of homogeneous Riemannian spaces with zero Ricci curvature, Funkcional. Anal. i PriloŽen. 9 (1975) 5 MR0402650
2 A L Besse, Einstein manifolds, Classics in Math., Springer (2008) MR2371700
3 D Birkes, Orbits of linear algebraic groups, Ann. of Math. $(2)$ 93 (1971) 459 MR0296077
4 C Böhm, M Wang, W Ziller, A variational approach for compact homogeneous Einstein manifolds, Geom. Funct. Anal. 14 (2004) 681 MR2084976
5 I Dotti Miatello, Ricci curvature of left invariant metrics on solvable unimodular Lie groups, Math. Z. 180 (1982) 257 MR661702
6 P Eberlein, Riemannian $2$–step nilmanifolds with prescribed Ricci tensor, from: "Geometric and probabilistic structures in dynamics" (editors K Burns, D Dolgopyat, Y Pesin), Contemp. Math. 469, Amer. Math. Soc. (2008) 167 MR2478470
7 P Eberlein, M Jablonski, Closed orbits of semisimple group actions and the real Hilbert–Mumford function, from: "New developments in Lie theory and geometry" (editors C S Gordon, J Tirao, J A Vargas, J A Wolf), Contemp. Math. 491, Amer. Math. Soc. (2009) 283 MR2537062
8 C S Gordon, E N Wilson, Isometry groups of Riemannian solvmanifolds, Trans. Amer. Math. Soc. 307 (1988) 245 MR936815
9 J Heber, Noncompact homogeneous Einstein spaces, Invent. Math. 133 (1998) 279 MR1632782
10 P Heinzner, G W Schwarz, H Stötzel, Stratifications with respect to actions of real reductive groups, Compos. Math. 144 (2008) 163 MR2388560
11 M Jablonski, Distinguished orbits of reductive groups, to appear in Rocky Mountain J. Math. arXiv:0806.3721
12 M Jablonski, Detecting orbits along subvarieties via the moment map, Münster J. Math. 3 (2010) 67
13 M Jablonski, Moduli of Einstein and non-Einstein nilradicals, Geom. Dedicata 152 (2011) 63
14 G R Jensen, Homogeneous Einstein spaces of dimension four, J. Differential Geometry 3 (1969) 309 MR0261487
15 G Kempf, L Ness, The length of vectors in representation spaces, from: "Algebraic geometry (Proc. Summer Meeting, Univ. Copenhagen, 1978)" (editor K Lønsted), Lecture Notes in Math. 732, Springer (1979) 233 MR555701
16 F C Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Math. Notes 31, Princeton Univ. Press (1984) MR766741
17 J Lauret, Ricci soliton homogeneous nilmanifolds, Math. Ann. 319 (2001) 715 MR1825405
18 J Lauret, On the moment map for the variety of Lie algebras, J. Funct. Anal. 202 (2003) 392 MR1990531
19 J Lauret, Einstein solvmanifolds and nilsolitons, from: "New developments in Lie theory and geometry" (editors C S Gordon, J Tirao, J A Vargas, J A Wolf), Contemp. Math. 491, Amer. Math. Soc. (2009) 1 MR2537049
20 J Lauret, Einstein solvmanifolds are standard, Ann. of Math. $(2)$ 172 (2010) 1859 MR2726101
21 J Lauret, Ricci soliton solvmanifolds, J. Reine Angew. Math. 650 (2011) 1
22 J Lauret, C Will, Einstein solvmanifolds: existence and non-existence questions, Math. Ann. 350 (2011) 199
23 A Marian, On the real moment map, Math. Res. Lett. 8 (2001) 779 MR1879820
24 J Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976) 293 MR0425012
25 G D Mostow, Self-adjoint groups, Ann. of Math. $(2)$ 62 (1955) 44 MR0069830
26 G D Mostow, Fully reducible subgroups of algebraic groups, Amer. J. Math. 78 (1956) 200 MR0092928
27 L Ness, A stratification of the null cone via the moment map, Amer. J. Math. 106 (1984) 1281 MR765581
28 Y Nikolayevsky, Einstein solvmanifolds attached to two-step nilradicals arXiv:0805.0646v1
29 Y Nikolayevsky, Einstein solvmanifolds with a simple Einstein derivation, Geom. Dedicata 135 (2008) 87 MR2413331
30 Y Nikolayevsky, Einstein solvmanifolds with free nilradical, Ann. Global Anal. Geom. 33 (2008) 71 MR2369187
31 Y Nikolayevsky, Einstein solvmanifolds and the pre-Einstein derivation, Trans. Amer. Math. Soc. 363 (2011) 3935
32 Y G Nikonorov, Noncompact homogeneous Einstein $5$–manifolds, Geom. Dedicata 113 (2005) 107 MR2171301
33 T L Payne, The existence of soliton metrics for nilpotent Lie groups, Geom. Dedicata 145 (2010) 71 MR2600946
34 R W Richardson, P J Slodowy, Minimum vectors for real reductive algebraic groups, J. London Math. Soc. $(2)$ 42 (1990) 409 MR1087217
35 R Sjamaar, Convexity properties of the moment mapping re-examined, Adv. Math. 138 (1998) 46 MR1645052
36 H Whitney, Elementary structure of real algebraic varieties, Ann. of Math. $(2)$ 66 (1957) 545 MR0095844
37 C Will, Rank-one Einstein solvmanifolds of dimension $7$, Differential Geom. Appl. 19 (2003) 307 MR2013098
38 C Will, A curve of nilpotent Lie algebras which are not Einstein nilradicals, Monatsh. Math. 159 (2010) 425 MR2600907