Bibliography of pertinent literature

Zhuang-dan Guan

• Positive Lemma, Generalized Extremal-solitons and Second Order Linear Differential Equations, preprint 2012, 17 pages.
• Toward a classification of compact real solvmanifolds with real symplectic structures, in preprint 2010, 23 pages.
• On Classification of Compact Complex Solvmanifolds, doi: 10.1016/j.jalgebra.2011.08.026, J. of Algebra, vol 347 (2011), 69--82.
• Toward a Classification of Symplectic Nilmanifolds, International Mathematical Research Notices, vol 2010 (2010), 4377--4384 2010:doi:10.1093/imrn/rnq049.
• Affine Compact Almost-Homogeneous Manifolds of Cohomogeneity One Central European Journal of Mathematics, vol 7 (2009), 84--123. Note: Theorem 10.2 is true when the manifold is Fano, cohomogeneity one and has a semisimple automorphism group.
• Classification of Compact Complex Homogeneous Manifolds with Pseudo-k\"ahlerian Structures, Jour. of Algebra, vol 324 (2010), 2010--2024; doi:10.1016/j.jalgebra.2010.06.013
• Classification of Compact Homogeneous Manifolds with Pseudo-k\"ahlerian Structures (Announcement) Comptes Rendus Math\'ematiques de l'Acad. Sci. Canada, vol 31 (2009), no. 1. 20--23.
• Modification and the Cohomology Groups of Compact Solvmanifolds, ERA-AMS 13 (2007), 74--81; see also Comments
• A Complete Classification of Compact Almost Homogeneous K\"ahler Manifolds of Cohomogeneity One with a Higher Codimensional End, in preparation.
• Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---I, Pacific J. of Appl. Math., vol 3 (2011), 43--72.
• Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---II, Pacific J. of Appl. Math., vol 3 (2011), 179--202.
• Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---III, in preprint 2010, 15 pages.
• Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One, Pacific J. of Mathematics, vol. 253 (2011), 293--422; doi:10.2140/pjm.2011.253.383.
• Moser Vector Field and Geometry of the Mabuchi Moduli Space of K\"ahler Metrics, in preprint 2003, 9 pages.
• Jacobi Fields and the Geodesic Stability, in preparation.
• Book cooperated with S. Kobayashi: Compact Complex Manifolds and K\"ahler Geometry, in process.
• Testing the Geodesic Stability on Toric Bundles, in preparation.
• Extremal-Solitons and Exponential C^{\infty} Convergence of Modified Calabi Flow on Certain CP^1 bundles, Pacific J. Math. vol. 233 (2007), 91-124.
• Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---IV, Ann. Glob. Anal. Geom. 30(2006), 139--167.
• An Inequality of Rozansky-Witten Invariants, in preparation.
• On Representation Theory and the Cohomology Rings of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Central European Journal of Mathematics, vol 1 (2003), 661--669.
• On the Betti Numbers of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Math. Res. Letters vol 8 (2001), 663--669.
• On Modified Mabuchi Functional and Mabuchi Moduli Spaces of K\"ahler Metrics on Toric Bundles. Math. Research Letters vol 6 (1999), 547--555.
• Quasi-Einstein Metrics and Evolution of Metrics in a K\"ahler Class, a preprint will come out soon.
• (with X. Chen) Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One, Asian J. Math. vol 4 (2000), 817--830..
• Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---II, Journal of Geometric Analysis, vol 12 (2002), 63--79. The final version before publication
• Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---III, International Journal of Mathematics, vol 14 (2003), 259--287. The final version before publication Note written on Feb. 14, 2007: The original paper was cut by the referees and the editors. Therefore, some information in the paper was missing. Here I found a pdf copy of an original source which was modified after receiving two preprints from Andrew Spiro and further discussions. It is apparently that the completion of the normal bundle of the exceptional divisor in section 6 is different from the projective normal bundle and our degeneration (if it actually exists) is a little different from that in the recent paper of J. Ross and R. P. Thomas (JDG 72 (2006), 429--466). Our condition is stronger than theirs.
• Toward a Classification of Compact Complex Homogeneous Manifolds, Journal of Algebra vol. 273 (2004), 33--59.
• Toward a Classification of Compact Complex Homogeneous Manifolds II, in preparation.
• On Compact Symplectic Manifolds with Lie Group Symmetries, Transactions of AMS. 357 (2005), 3359-3373.
• Classification of Compact Contact Homogeneous Spaces, a preprint will come out soon.
• Classification of Compact Complex Homogeneous Spaces with Invariant Volumes, Transactions of AMS. 354(2002) 4493-4504. Announcement appeared in ERA-AMS vol 3 (1997), 90-92.
• Classification of Compact Homogeneous Spaces with Invariant Symplectic Structures, ERA-AMS vol 3 (1997), 52-54.
• Toward a Classification of Almost Homogeneous Manifolds II---Bad Models, International J. Math., vol 10 (1999), 571--586.
• Toward a Classification of Almost Homogeneous Manifolds III---SL(2)xC* Actions, International J. Math., vol 11 (2000), 799--809.
• A Splitting Theorem for Compact Complex Homogeneous Space with a Symplectic Structure, Geometrica Dedicata vol. 63(1996), 217-225. MR 98a:53105.
• Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure II, Invent. Math. vol. 121(1995), 135-145. (see also F. Bogomolov: On Guan's Examples of Simply Connected Non-K\"ahler Compact Complex Manifolds, Amer. J. Math. 118(1996), 1037-1046). MR 97i:32033.
• Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure III, International J. of Math. vol. 6(1995), 709-718. MR 97i:32034.
• Examples of Compact Holomorphic Symplectic Manifolds Which Are Not K\"ahlerian, (In Geometry and Analysis on Complex Manifolds---Festschift for Professor S. Kobayashi's 60-th birthday, World Scientific Publishing Co. 1994), 63-74.
• Existence of Extremal Metrics on Almost Homogeneous Spaces with Two Ends. Transaction of AMS, vol. 347(1995), 2255-2262.
• Quasi-Einstein Metrics, International J. of Math., vol. 6(1995), 371-379. MR 96e:53060.
• Stablity of Hermitian Vector Bundles, a Quantitative Point of View, Intern'l J. Math. 3 (1992), 477-481. MR 93k:32067.
• Toward a Classification of Almost Homogeneous Manifolds I---Linearization of the Singular Extremal Rays. International J. of Math., vol 8(1997), 999-1014.
• (with Dorfmeister) Fine Structures of Reductive Pseudo-K\"ahlerian Spaces, Geometrica Dedicata 39 (1991), 321-338. MR 92h:53081.
• (with Dorfmeister) Pseudo-K\"ahlerian Homogeneous Spaces Admitting a Reductive Transitive Group of Automorphisms, Math. Zeitschrift 209 (1992), 89-100. MR 92k:32058.
• (with Dorfmeister) Classification of Compact Homogeneous Pseudo-K\"ahler Manifolds, Comm. Math. Helv. 67 (1992), 499-513. MR 93i:32042.(see also Huckleberry A. L.: Homogeneous Pseudo-K\"ahlerian Manifolds: A Hamiltonian Viewpoint, Note di Matematica 10(1990) suppl. 2. 337-342. MR 94f:53052).
• Curvature on the Hermitian Symmetric Spaces. Acta Math. Sinica. New Series 4 (1988), 270-283.

Zhuang-dan Guan, Department of Mathematics, University of California at Riverside, Riverside, CA 92521, U.S.A.

e-mail: zguan@math.ucr.edu

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