Solitony Ricciego

• Autorzy: Derdziński A.
• Języki publikacji: PL

Słowa kluczowe

PL

potok Ricciego; rozmaitości zwarte; metryki Einsteina; solitony Kählera-Ricciego

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2012
• Tom: T. 48, Nr 1
• Strony: 1--32
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Derdziński A.

• The Ohio State University

Bibliografia

• [1] T. Aubin, Equations du type Monge-Ampere sur les varietes kahleriennes compactes, Bull. Sci. Math. 102 (1978), nr 1, 63-95.
• [2] S. Bando, T. Mabuchi, Uniqueness of Einstein Kahler metrics modulo connected group actions, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., t. 10, North-Holland, Amsterdam, 1987, 11-40.
• [3] A. Barros, E. Ribeiro, Some characterizations for compact almost Ricci solitons, Proc. Amer. Math. Soc. 140 (2012), nr 3, 1033-1040.
• [4] L. Berard Bergery, Sur de nouvelles varietes riemanniennes d’Einstein, Inst. Elie Cartan, t. 6, Univ. Nancy, Nancy, 1982, 1-60.
• [5] A. L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, t. 10, Springer-Verlag, Berlin 1987.
• [6] J, P. Bourguignon, L’espace des metriques riemanniennes d’une variete cumpactc, These d’Etat, Univwsite Paris VII (1974).
• [7] E. Calabi, On Kahler manifolds with vanishing canonical class, Algebraic geometry and topology, a symposium in honor of S. Lefschetz, Princeton University Press, Princeton, NJ, 1957, 78-89.
• [8] H.-D. Cao, Existence of gradient Kahler-Ricci solitons, Elliptic and parabolic methods in geometry (Minneapolis, MN, 1994), A. K. Peters, Wellesley, MA, 1996, 1- 16.
• [9] H.-D. Cao, Recent progress on Ricci solitons, Recent advances in geometric analysis, Adv. Lect. Math. (ALM), t. 11, Int. Press, Somerville, MA, 2010, 1-38.
• [10] B. Chow, Ricci flow and Einstein metrics in low dimensions, Surveys in differential geometry: essays on Einstein manifolds, Surv. Differ. Geom., VI, Int. Press, Boston, MA, 1999, 187-220.
• [11] A. Dancer, M. Wang, On Ricci solitons of cohomogeneity one, Ann. Global Anal. Geom. 39 (2011), nr 3, 259-292.
• [12] A. Derdziński, G. Maschler, Local classification of conformally-Einstein Kähler metrics in higher dimensions, Proc. London Math. Soc. 87 (2003), nr 3, 779-819.
• [13] A. Derdziński, G. Maschler, Special Kahler-Ricci potentials on compact Kahler manifolds, J. Reine Angew. Math. 593 (2006), 73-116.
• [14] F. J. E. Dillen, L. C. A. Verstraelen (red.), Handbook of differential geometry., t. I, North-Holland, Amsterdam 2000.
• [15] P. Federbush, Partially alternate derivation of a result of Nelson, J. Mathematical Phys. 10 (1969), nr 1, 50-52.
• [16] M. Feldman, T. Ilmanen, D. Knopf, Rotationally symmetric shrinking and expanding gradient Kahler-Ricci solitons, J. Differential Geom. 65 (2003), nr 2, 169-209.
• [17] M. Fernandez-López, E. Garcfa-Rio, A remark on compact Ricci solitons, Math. Ann. 340 (2008), nr 4, 893-896.
• [18] D.H. Friedan, Nonlinear models in 2 + Ɛ dimensions, Ann. Physics 163 (1985), nr 2, 318-419.
• [19] L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), nr 4, 1061-1083.
• [20] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), nr 2, 255-306.
• [21] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math., t. 71, Amer. Math. Soc., Providence, RI, 1988, 237-262.
• [22] T. Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993), nr 4, 301-307.
• [23] S. Kobayashi, T. Ochiai, Characterizations of complex projective spaces and hyperquadrics J. Math Kyoto Univ. 13 (1973), nr 1, 31-47.
• [24] N. Koiso, On rotationally symmetric Hamilton's equation for Kähler-Einstein metrics, Recent topics in differential and analytic geometry, Adv. Stud. Pure Math., t. 18, Academic Press, Boston, MA, 1990, 327-337.
• [25] C. Li, On rotationally symmetric Kähler-Ricci solitons, preprint arXiv:1004.4049 (2010).
• [26] X.-M. Li, On extensions of Myers’ theorem, Bull. London Math. Soc. 27 (1995), nr 4, 392-396.
• [27] G. Maschler, Special Kähler-Ricci potentials and Ricci solitons, Ann. Global Anal. Geom. 34 (2008), nr 4, 367-380.
• [28] D. N. Page, A compact rotating gravitational instanton, Phys. Lett. B 79 (1978), nr 3, 235-238.
• [29] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint, arXiv:math.DG/0211159.
• [301 G. Perelman, Ricci flow with surqeru on three-manifolds, preprint, arXiv : math. DG/0303109.
• [31] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint, arXiv:math.DG/0307245.
• [32] S. Pigola, M. Rigoli, M. Rimoldi, A. G. Setti, Ricci almost solitons, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (2011), nr 4, 757-799.
• [33] O. S. Rothaus, Logarithmic Sobolev inequalities and the spectrum of Schródinger operators, J. Funct. Anal. 42 (1981), nr 1, 110-120.
• [34] G. Tian, informacja przekazana ustnie (2005).
• [35] G. Tian, X. Zhu, A new holomorphic invariant and uniqueness of Kähler-Ricci solitons, Comment. Math. Helv. 77 (2003), nr 2. 297 325
• [36] X.-J. Wang, X. Zhu, Kähler-Ricci solitons on toric manifolds with positive first Chem class, Adv. Math. 188 (2004), nr 1, 87-103.
• [37] S. T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation. I, Comm. Pure Appl. Math. 31 (1978), nr 3, 339-411.
• [38] Z. Zhang, On the finiteness of the fundamental group of a compact shrinking Ricci soliton, Colloq. Math. 107 (2007), nr 2, 297-299.