메뉴 건너뛰기




Volumn 319, Issue 4, 2001, Pages 715-733

Ricci soliton homogeneous nilmanifolds

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035607186     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004456     Document Type: Article
Times cited : (208)

References (36)
  • 1
    • 0003207990 scopus 로고
    • Generalized Heisenberg groups and Damek-Ricci harmonic spaces
    • Springer-Verlag Berlin Heidelberg
    • J. Berndt, F. Tricerri, L. Vanhecke, Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Lect. Notes in Math. 1598 (1995), Springer-Verlag Berlin Heidelberg
    • (1995) Lect. Notes in Math. , vol.1598
    • Berndt, J.1    Tricerri, F.2    Vanhecke, L.3
  • 2
    • 0003339730 scopus 로고
    • Einstein manifolds
    • Springer-Verlag, Berlin-Heidelberg
    • A. Besse, Einstein manifolds, Ergeb. Math. 10 (1987), Springer-Verlag, Berlin-Heidelberg
    • (1987) Ergeb. Math. , vol.10
    • Besse, A.1
  • 3
    • 0002397508 scopus 로고
    • Ricci curvature and Einstein metrics
    • Springer-Verlag
    • J.P. Bourguignon, Ricci curvature and Einstein metrics, Lect. Notes in Math. 838 (1981), 42-63, Springer-Verlag
    • (1981) Lect. Notes in Math. , vol.838 , pp. 42-63
    • Bourguignon, J.P.1
  • 5
    • 0000965396 scopus 로고
    • Extremal Kähler metrics
    • Seminar. on Differential Geometry (ed. by S. Yau), Princeton Univ. Press., Princeton
    • E. Calabi, Extremal Kähler metrics, in Seminar. on Differential Geometry (ed. by S. Yau), Ann. Math. Studies 102 (1982), 259-290, Princeton Univ. Press., Princeton
    • (1982) Ann. Math. Studies , vol.102 , pp. 259-290
    • Calabi, E.1
  • 7
    • 0000820709 scopus 로고
    • On Harnack's inequalities for the Kähler-Ricci flow
    • H-D. Cao, On Harnack's inequalities for the Kähler-Ricci flow, Inventiones Math. 109 (1992), 247-263
    • (1992) Inventiones Math. , vol.109 , pp. 247-263
    • Cao, H.-D.1
  • 8
    • 0031063197 scopus 로고    scopus 로고
    • Limits of solutions to the Kähler Ricci flow
    • H-D. Cao, Limits of solutions to the Kähler Ricci flow, J. Differential Geom. 45 (1997), 257-272
    • (1997) J. Differential Geom. , vol.45 , pp. 257-272
    • Cao, H.-D.1
  • 10
    • 0033477993 scopus 로고    scopus 로고
    • Recent developments on the Ricci flow
    • H-D. Cao, B. Chow, Recent developments on the Ricci flow, Bull. Amer. Math. Soc. 36 (1999), 59-74
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 59-74
    • Cao, H.-D.1    Chow, B.2
  • 11
    • 0030569237 scopus 로고    scopus 로고
    • On a class of compact and non-compact quasi-Einstein metrics and their renormalizabilityproperties
    • T. Chave, G. Valent, On a class of compact and non-compact quasi-Einstein metrics and their renormalizabilityproperties, Nuclear Physics B 478 (1996), 758-778
    • (1996) Nuclear Physics B , vol.478 , pp. 758-778
    • Chave, T.1    Valent, G.2
  • 12
    • 0009423544 scopus 로고
    • Naturally reductive metrics and Einstein metrics on compact lie groups
    • J. D'Atri, W. Ziller, Naturally reductive metrics and Einstein metrics on compact lie groups, Memoirs Amer. Math. Soc. 18 (1979) No. 215
    • (1979) Memoirs Amer. Math. Soc. , vol.18 , Issue.215
    • D'Atri, J.1    Ziller, W.2
  • 13
    • 0003294608 scopus 로고    scopus 로고
    • Geometry of nonpositively curved manifolds
    • The University of Chicago Press., Chicago
    • P. Eberlein, Geometry of nonpositively curved manifolds, Chicago Lectures in Mathematics, The University of Chicago Press., Chicago (1996)
    • (1996) Chicago Lectures in Mathematics
    • Eberlein, P.1
  • 14
    • 0030487357 scopus 로고    scopus 로고
    • Quarter pinched homogeneous spaces of negative curvature
    • P. Eberlien, J. Heber, Quarter pinched homogeneous spaces of negative curvature, International J. Math. 7 (1996), 441-500
    • (1996) International J. Math. , vol.7 , pp. 441-500
    • Eberlien, P.1    Heber, J.2
  • 15
    • 0011504985 scopus 로고
    • Nonlinear models in 2 + ε dimensions
    • D. Friedan, Nonlinear models in 2 + ε dimensions, Ann. of Physics 163 (1985), 318-419
    • (1985) Ann. of Physics , vol.163 , pp. 318-419
    • Friedan, D.1
  • 17
    • 0000389226 scopus 로고
    • Variété des lois d'algébres de Lie nilpotentes
    • Y. Hakimjanov, Variété des lois d'algébres de Lie nilpotentes, Geom. Dedicata 40 (1991), 269-295
    • (1991) Geom. Dedicata , vol.40 , pp. 269-295
    • Hakimjanov, Y.1
  • 18
    • 84972513449 scopus 로고
    • Three-manifolds with positive Ricci curvature
    • R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306
    • (1982) J. Differential Geom. , vol.17 , pp. 255-306
    • Hamilton, R.1
  • 19
    • 0000872141 scopus 로고
    • The Ricci flow on surfaces
    • R. Hamilton, The Ricci flow on surfaces, Contemporary Math. 71 (1988), 237-261
    • (1988) Contemporary Math. , vol.71 , pp. 237-261
    • Hamilton, R.1
  • 20
    • 0001825291 scopus 로고
    • The formation of singularities in the Ricci flow
    • R. Hamilton, The formation of singularities in the Ricci flow, Surveys in Differential Geometry II (1995), 7-136
    • (1995) Surveys in Differential Geometry , vol.2 , pp. 7-136
    • Hamilton, R.1
  • 21
    • 0032387785 scopus 로고    scopus 로고
    • Noncompact homogeneous Einstein spaces
    • J. Heber, Noncompact homogeneous Einstein spaces, Inventiones Math. 133 (1998), 279-352
    • (1998) Inventiones Math. , vol.133 , pp. 279-352
    • Heber, J.1
  • 22
    • 19644372179 scopus 로고    scopus 로고
    • in preparation
    • J. Heber, in preparation
    • Heber, J.1
  • 23
  • 24
    • 0040863526 scopus 로고
    • Ricci solitons on compact three-manifolds
    • T. Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993), 301-307
    • (1993) Differential Geom. Appl. , vol.3 , pp. 301-307
    • Ivey, T.1
  • 25
    • 84966206339 scopus 로고
    • New examples of complete Ricci solitons
    • T. Ivey, New examples of complete Ricci solitons, Proc. Amer. Math. Soc. 122 (1994), 241-245
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 241-245
    • Ivey, T.1
  • 26
    • 0030265973 scopus 로고    scopus 로고
    • Local existence of Ricci solitons
    • T. Ivey, Local existence of Ricci solitons, Manuscripta Math. 91 (1996), 151-162
    • (1996) Manuscripta Math. , vol.91 , pp. 151-162
    • Ivey, T.1
  • 27
    • 21744438896 scopus 로고    scopus 로고
    • Ricci solitons on compact Kähler surfaces
    • T. Ivey, Ricci solitons on compact Kähler surfaces, Proc. A.M.S. 125 (1997), 1203-1208
    • (1997) Proc. A.M.S. , vol.125 , pp. 1203-1208
    • Ivey, T.1
  • 28
    • 0004293970 scopus 로고
    • Interscience Publishers, New York
    • N. Jacobson, Lie algebras, Interscience Publishers, New York (1962)
    • (1962) Lie Algebras
    • Jacobson, N.1
  • 29
    • 0007551329 scopus 로고
    • The scalar curvature of left-invariant Riemannian metrics
    • G. Jensen, The scalar curvature of left-invariant Riemannian metrics, Indiana Math. J. 20 (1971), 1125-1144
    • (1971) Indiana Math. J. , vol.20 , pp. 1125-1144
    • Jensen, G.1
  • 30
    • 0000841192 scopus 로고
    • Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms
    • A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc. 258 (1980), 147-153
    • (1980) Trans. Amer. Math. Soc. , vol.258 , pp. 147-153
    • Kaplan, A.1
  • 31
    • 0000307628 scopus 로고
    • On rotationally symmetric Hamilton's equation for Kähler-Einstein metrics
    • N. Koiso, On rotationally symmetric Hamilton's equation for Kähler-Einstein metrics, Adv. Studies in Pure math. 18-1 (1990), 327-337
    • (1990) Adv. Studies in Pure Math. , vol.18 , Issue.1 , pp. 327-337
    • Koiso, N.1
  • 32
    • 0040629820 scopus 로고    scopus 로고
    • Homogeneous nilmanifolds attached to representations of compact Lie groups
    • J. Lauret, Homogeneous nilmanifolds attached to representations of compact Lie groups, Manuscripta Math. 99 (1999), 287-309
    • (1999) Manuscripta Math. , vol.99 , pp. 287-309
    • Lauret, J.1
  • 33
    • 0001582143 scopus 로고
    • Curvature of Left-invariant Metrics on Lie Groups
    • J. Milnor, Curvature of Left-invariant Metrics on Lie Groups, Adv. in Math. 21 (1976), 293-329
    • (1976) Adv. in Math. , vol.21 , pp. 293-329
    • Milnor, J.1
  • 34
    • 0000485144 scopus 로고
    • On the derivation algebras of Lie algebras
    • S. Togo, On the derivation algebras of Lie algebras, Canadian J. Math., 13 (1961), 201-216
    • (1961) Canadian J. Math. , vol.13 , pp. 201-216
    • Togo, S.1
  • 35
    • 0001540523 scopus 로고
    • Isometry groups on homogeneous nilmanifolds
    • E. Wilson, Isometry groups on homogeneous nilmanifolds, Geom. Dedicata 12 (1982), 337-346
    • (1982) Geom. Dedicata , vol.12 , pp. 337-346
    • Wilson, E.1
  • 36
    • 51249174219 scopus 로고
    • Einstein metrics on solvable groups
    • T. Wolter, Einstein metrics on solvable groups, Math. Z. 206 (1991), 457-471
    • (1991) Math. Z. , vol.206 , pp. 457-471
    • Wolter, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.