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Volumn 188, Issue 1, 2004, Pages 87-103

Kähler-Ricci solitons on toric manifolds with positive first Chern class

Author keywords

K hler Ricci soliton; Monge Amp re equation; Toric Fano manifold

Indexed keywords


EID: 4444346223     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2003.09.009     Document Type: Article
Times cited : (318)

References (29)
  • 1
    • 0002260507 scopus 로고
    • Equations du type Monge-Ampère sur les variétés kählériennes compactes
    • (French)
    • Aubin T. Equations du type Monge-Ampère sur les variétés kählériennes compactes (French) Bull. Sci. Math. 102 2 1978 63-95
    • (1978) Bull. Sci. Math. , vol.102 , Issue.2 , pp. 63-95
    • Aubin, T.1
  • 2
    • 0002008201 scopus 로고
    • Uniqueness of Einstein Kähler metrics modulo connected group actions. Algebraic geometry
    • (Sendai, 1985)
    • Bando S. Mabuchi T. Uniqueness of Einstein Kähler metrics modulo connected group actions. Algebraic geometry (Sendai, 1985) Adv. Stud. Pure Math. 10 1987 11-40
    • (1987) Adv. Stud. Pure Math. , vol.10 , pp. 11-40
    • Bando, S.1    Mabuchi, T.2
  • 4
    • 0001225768 scopus 로고    scopus 로고
    • On the classification of toric Fano 4-folds
    • Batyrev V.V. On the classification of toric Fano 4-folds J. Math. Sci. 94 1999 1021-1050
    • (1999) J. Math. Sci. , vol.94 , pp. 1021-1050
    • Batyrev, V.V.1
  • 5
    • 0033473251 scopus 로고    scopus 로고
    • Einstein-Kähler metrics on symmetric toric Fano manifolds
    • Batyrev V.V. Selivanova E.N. Einstein-Kähler metrics on symmetric toric Fano manifolds J. Reine Angew. Math. 512 1999 225-236
    • (1999) J. Reine Angew. Math. , vol.512 , pp. 225-236
    • Batyrev, V.V.1    Selivanova, E.N.2
  • 6
    • 0031063197 scopus 로고    scopus 로고
    • Limits of solutions of the Kähler - Ricci flow
    • Cao H.D. Limits of solutions of the Kähler-Ricci flow J. Differential Geom. 45 1997 257-272
    • (1997) J. Differential Geom. , vol.45 , pp. 257-272
    • Cao, H.D.1
  • 8
    • 4243659282 scopus 로고
    • Nonlinear models in 2 + E dimensions
    • Friedan D. Nonlinear models in 2 + E dimensions Phys. Rev. Lett. 45 1980 1057-1060
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 1057-1060
    • Friedan, D.1
  • 9
    • 0038880355 scopus 로고
    • An obstruction to the existence of Kähler - Einstein metrics
    • Futaki A. An obstruction to the existence of Kähler-Einstein metrics Invent. Math. 73 1983 437-443
    • (1983) Invent. Math. , vol.73 , pp. 437-443
    • Futaki, A.1
  • 10
    • 0001825291 scopus 로고
    • Formation of singularities in the Ricci-flow
    • Hamilton R.S. Formation of singularities in the Ricci-flow Surveys Differential Geom. 2 1995 7-136
    • (1995) Surveys Differential Geom. , vol.2 , pp. 7-136
    • Hamilton, R.S.1
  • 11
    • 0000307628 scopus 로고
    • On rotationally symmetric Hamilton's equation for Kähler - Einstein metrics, Recent topics in differential and analytic geometry
    • Koiso N. On rotationally symmetric Hamilton's equation for Kähler-Einstein metrics, Recent topics in differential and analytic geometry Adv. Stud. Pure Math. 18 1990 327-337
    • (1990) Adv. Stud. Pure Math. , vol.18 , pp. 327-337
    • Koiso, N.1
  • 12
    • 4444356844 scopus 로고    scopus 로고
    • The intermediate Christoffel - Minkowski problem
    • preprint
    • Ma X.N. Trudinger N.S. Wang X.-J. The intermediate Christoffel-Minkowski problem, preprint
    • Ma, X.N.1    Trudinger, N.S.2    Wang, X.-J.3
  • 13
    • 84972552050 scopus 로고
    • Einstein - Kähler forms, Futaki invariants and convex geometry on toric Fano varieties
    • Mabuchi T. Einstein-Kähler forms, Futaki invariants and convex geometry on toric Fano varieties Osaka J. Math. 24 1987 705-737
    • (1987) Osaka J. Math. , vol.24 , pp. 705-737
    • Mabuchi, T.1
  • 14
    • 84972537159 scopus 로고
    • Sur la structure du group d'homéomorphismes analytiques d'une certaine variété kählérienne
    • Matsushima Y. Sur la structure du group d'homéomorphismes analytiques d'une certaine variété kählérienne Nagoya Math. J. 11 1957 145-150
    • (1957) Nagoya Math. J. , vol.11 , pp. 145-150
    • Matsushima, Y.1
  • 16
    • 84972576629 scopus 로고
    • Einstein - Kähler toric Fano manifolds
    • Nakagawa Y. Einstein-Kähler toric Fano manifolds Töhoku Math. J. 45 1993 297-310
    • (1993) Töhoku Math. J. , vol.45 , pp. 297-310
    • Nakagawa, Y.1
  • 17
    • 84972565481 scopus 로고
    • Classification of Einstein - Kähler toric Fano manifolds
    • Nakagawa Y. Classification of Einstein-Kähler toric Fano manifolds Töhoku Math. J. 46 1994 125-133
    • (1994) Töhoku Math. J. , vol.46 , pp. 125-133
    • Nakagawa, Y.1
  • 21
    • 38249010950 scopus 로고
    • Métriques d'Einstein - Kähler sur des variétés aṕremiére classe de Chern positive
    • Real C. Métriques d'Einstein-Kähler sur des variétés aṕremiére classe de Chern positive J. Funct. Anal. 106 1992 145-188
    • (1992) J. Funct. Anal. , vol.106 , pp. 145-188
    • Real, C.1
  • 22
    • 0000858517 scopus 로고
    • The existence of Kähler - Einstein metrics on manifolds with positive anti-canonical line bundle and a suitable finite symmetry group
    • Siu Y.T. The existence of Kähler-Einstein metrics on manifolds with positive anti-canonical line bundle and a suitable finite symmetry group Ann. of Math. 127 2 1988 585-627
    • (1988) Ann. of Math. , vol.127 , Issue.2 , pp. 585-627
    • Siu, Y.T.1
  • 23
    • 0001984784 scopus 로고
    • On Calabi's conjecture for complex surfaces
    • Tian G. On Calabi's conjecture for complex surfaces Invent. Math. 101 1990 101-172
    • (1990) Invent. Math. , vol.101 , pp. 101-172
    • Tian, G.1
  • 24
    • 0038967641 scopus 로고    scopus 로고
    • Kähler - Einstein metrics with positive scalar curvature
    • Tian G. Kähler-Einstein metrics with positive scalar curvature Invent. Math. 130 1997 1-37
    • (1997) Invent. Math. , vol.130 , pp. 1-37
    • Tian, G.1
  • 26
    • 0001336740 scopus 로고    scopus 로고
    • Uniqueness of Kähler - Ricci solitons
    • Tian G. Zhu X.H. Uniqueness of Kähler-Ricci solitons Acta Math. 184 2000 271-305
    • (2000) Acta Math. , vol.184 , pp. 271-305
    • Tian, G.1    Zhu, X.H.2
  • 27
    • 0036444098 scopus 로고    scopus 로고
    • A new holomorphic invariant and uniqueness of Kähler - Ricci solitons
    • Tian G. Zhu X.H. A new holomorphic invariant and uniqueness of Kähler-Ricci solitons Comm. Math. Helv. 77 2002 297-325
    • (2002) Comm. Math. Helv. , vol.77 , pp. 297-325
    • Tian, G.1    Zhu, X.H.2
  • 28
    • 84980156699 scopus 로고
    • On the Ricci curvature of a compact Kähler manifold and the complex Monge - Ampère equation, I
    • Yau S.T. On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I Comm. Pure Appl. Math. 31 1978 339-411
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 339-411
    • Yau, S.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.