Usher M. Kodaira dimension and symplectic sums[J]. Commentarii Mathematici Helvetici, 2009, 84(1): 57-85.
2
Friedl S, Vidussi S. Symplectic 4-manifolds with a free circle action[C]., 2008.
3
Fine J. A gauge theoretic approach to the anti-self-dual Einstein equations[C]., 2011.
4
Friedl S, Vidussi S. On the topology of Symplectic Calabi-Yau 4-manifolds[J]. Journal of Topology, 2012, 6(4): 945-954.
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Yau S. A survey of Calabi-Yau manifolds[C]., 2008, 13(1): 277-318.
6
Nobuhiro Nakamura. Bauer–Furuta invariants under {\mathbb{Z}_2} -actions. 2008.
7
Ishida M, Sasahira H. Stable Cohomotopy Seiberg-Witten Invariants of Connected Sums of Four-Manifolds with Positive First Betti Number[C]., 2008.
8
Nobuhiro Nakamura. BAUER-FURUTA INVARIANTS UNDER Z2-ACTIONS. 2008.
9
Baykur R I. Virtual Betti numbers and the symplectic Kodaira dimension of fibered 4-manifolds[J]. Proceedings of the American Mathematical Society, 2014, 142(12): 4377-4384.
10
Nobuhiro Nakamura. Bauer-Furuta invariants under Z_2-actions. 2007.
An odd Seiberg-Witten invariant imposes bounds on the signature of a closed, almost complex 4-manifold with vanishing first
Chern class. This applies in particular to symplectic 4-manifolds of Kodaira dimension zero.
In this paper, we prove a scalar curvature rigidity result for geodesic balls in Sn. This result contrasts sharply with the counterexamples to Min-Oo’s conjecture constructed in [7].
Suarezserrato P, Tapie S. Conformal entropy rigidity through Yamabe flows[J]. Mathematische Annalen, 2011, 353(2): 333-357.
2
Zimmer A M. Compact asymptotically harmonic manifolds[J]. Journal of Modern Dynamics, 2012, 6(3): 377-403.
3
Francoise D, Marc P, Andrea S, et al. On the horoboundary and the geometry of rays of negatively curved manifolds[J]. Pacific Journal of Mathematics, 2010, 259(1): 55-100.
4
Ledrappier F, Shu L. Entropy rigidity of symmetric spaces without focal points[J]. Transactions of the American Mathematical Society, 2012, 366(7): 3805-3820.
5
Itoh M, Satoh H, Suh Y J, et al. Horospheres and hyperbolicity of Hadamard manifolds[J]. Differential Geometry and Its Applications, 2014: 50-68.
6
Zimmer A M. Boundaries of non-compact harmonic manifolds[J]. Geometriae Dedicata, 2012, 168(1): 339-357.
7
Wang X. Compactifications of Complete Riemannian manifolds and Their Applications[C]., 2010.
8
Seonhee Lim. ENTROPY RIGIDITY FOR METRIC SPACES. 2012.
9
Heim B, Murase A. Max-Planck-Institut für Mathematik Bonn[C]., 2010.
10
Kotschick D. Entropies, Volumes, and Einstein Metrics[C]., 2004: 39-54.
Knopf D, Young A. Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric[J]. Proceedings of the American Mathematical Society, 2006, 137(2): 699-709.
2
Farrell F T, Ontaneda P. On the moduli space of negatively curved metrics of a hyperbolic manifold[J]. Journal of Topology, 2008, 3(3): 561-577.
3
Tom Farrell · P Ontaneda. Teichmüller Spaces and Negatively Curved Fiber Bundles. 2010.
4
Farrell F T, Gogolev A. The space of Anosov diffeomorphisms[J]. Journal of The London Mathematical Society-second Series, 2012, 89(2): 383-396.
5
Farrell F T, Gogolev A. On bundles that admit fiberwise hyperbolic dynamics[J]. Mathematische Annalen, 2014: 401-438.
6
Belegradek I, Hu J. Connectedness properties of the space of complete nonnegatively curved planes[J]. Mathematische Annalen, 2013: 1273-1286.
7
Tom Farrellaffiliated Withsuny. Teichmüller Spaces and Negatively Curved Fiber Bundles. 2010.
8
Deblois J, Knopf D, Young A, et al. Cross curvature flow on a negatively curved solid torus[J]. Algebraic \u0026 Geometric Topology, 2009, 10(1): 343-372.
9
Davis J F. The work of Tom Farrell and Lowell Jones in topology and geometry[J]. Pure and Applied Mathematics Quarterly, 2010, 8(1): 1-14.
10
Huang H. Four-orbifolds with positive isotropic curvature[J]. Frontiers of Mathematics in China, 2011, 11(5): 1123-1149.
In this article we show that any hyperbolic Inoue surface (also called Inoue-Hirzebruch surface of even type) admits anti-self-dual
bihermitian structures. The same result holds for any of its small deformations as far as its anti-canonical system is non-empty. Similar
results are obtained for parabolic Inoue surfaces. Our method also yields a family of anti-self-dual hermitian metrics on any half Inoue surface. We use the twistor method of Donaldson-Friedman [13] for the proof.