참고문헌
- M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379-392. https://doi.org/10.4310/jdg/1214429060
- P. Butzer and H. Johnen, Lipschitz spaces on compact manifolds, J. Functional Analysis 7 (1971), 242-266. https://doi.org/10.1016/0022-1236(71)90034-6
- Q. H. Cai and P. B. Zhao, Stability of quasi-DeTurck flows in Riemannian manifolds of quasi-constant sectional curvatures, Chinese Ann. Math. Ser. A 29 (2008), no. 1, 97-106.
- H. D. Cao and B. Chow, Recent developments on the Ricci flow, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 1, 59-74. https://doi.org/10.1090/S0273-0979-99-00773-9
- B. Chow and D. Knopf, The Ricci flow: An introduction, Mathematical Surveys and Monographs, 110. American Mathematical Society, Providence, RI, 2004.
- G. Da Prato and A. Lunardi, Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space, Arch. Rational Mech. Anal. 101 (1988), no. 2, 115-141. https://doi.org/10.1007/BF00251457
- M. DeTurck, Deforming metrics in the direction of their Ricci tensors, J. Differential Geom. 18 (1983), no. 1, 157-162. https://doi.org/10.4310/jdg/1214509286
- G. Dore and A. Favini, On the equivalence of certain interpolation methods, Boll. Un. Mat. Ital. B (7) 1 (1987), no. 4, 1227-1238.
- J. Eells and J. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. https://doi.org/10.2307/2373037
- C. Guenther, J. Isenberg, and D. Knopf, Stability of the Ricci flow at Ricci-flat metrics, Comm. Anal. Geom. 10 (2002), no. 4, 741-777. https://doi.org/10.4310/CAG.2002.v10.n4.a4
- R. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 65-222. https://doi.org/10.1090/S0273-0979-1982-15004-2
- R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255-306. https://doi.org/10.4310/jdg/1214436922
- R. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153-179. https://doi.org/10.4310/jdg/1214440433
- R. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz, CA, 1986), 237-262, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, 1988.
- R. Hamilton, The formation of singularities in the Ricci flow, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 7-136, Int. Press, Cambridge, MA, 1995
- R. Hamilton, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom. 7 (1999), no. 4, 695-729. https://doi.org/10.4310/CAG.1999.v7.n4.a2
- D. Henry, Geometric Theorem of Semilinear Parabolic Equations, Springer Verlag, Berlin, 1981.
- J. Isenberg and M. Jackson, Ricci flow of locally homogeneous geometries on closed manifolds, J. Differential Geom. 35 (1992), no. 3, 723-741. https://doi.org/10.4310/jdg/1214448265
- J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. https://doi.org/10.2307/1994022
- R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), no. 2, 479-495. https://doi.org/10.4310/jdg/1214439291
- G. Simonett, Center manifolds for quasilinear reaction-diffusion systems, Differential Integral Equations 8 (1995), no. 4, 753-796.
- H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Second edition. Johann Ambrosius Barth, Heidelberg, 1995.
- K. Yano, Differential Geometry on Complex and Almost Complex Spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 49 A Pergamon Press Book. The Macmillan Co., New York 1965.
- R. Ye, Ricci flow, Einstein metrics and space forms, Trans. Amer. Math. Soc. 338 (1993), no. 2, 871-896. https://doi.org/10.2307/2154433
- P. B. Zhao and H. Z. Song, Quasi-Einstein hypersurfaces in a hyperbolic space, Chinese Quart. J. Math. 13 (1998), no. 2, 49-52.
- P. B. Zhao and X. P. Yang, On quasi-Einstein field equation, Northeast. Math. J. 21 (2005), no. 4, 411-420.
- P. B. Zhao and X. P. Yang, On stationary hypersurfaces in Euclidean spaces, Acta Math. Sci. Ser. B Engl. Ed. 26 (2006), no. 2, 349-357. https://doi.org/10.1016/S0252-9602(06)60057-X
피인용 문헌
- On Intrinsic Properties of Ricci Flow Curve vol.41, pp.1, 2017, https://doi.org/10.1007/s40995-017-0213-1