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Cited by 45

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On the stability of Riemannian manifold with parallel spinors

Dai, Xianzhe, Wang, Xiaodong, Wei, Guofang·2005·Inventiones mathematicae
DOI 10.1007/s00222-004-0424-x
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Research works printed but not linked: 37

  1. Belegradek, I., Wei, G.: Metrics of positive Ricci curvature on bundles. Int. Math. Res. Not. 2004, 56–72 (2004) · DOI
  2. Bogomolov, F.A.: Hamiltonian Kähler manifolds. Dokl. Akad. Nauk SSSR 243, 1101–1104 (1978)
  3. Brooks, R.: The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv. 56, 581–598 (1981) · DOI · Paper page
  4. Bryant, R.: Metrics with exceptional holonomy. Ann. Math. (2) 126, 525–576 (1987) · DOI
  5. Bryant, R.: Some remarks on G2 manifolds. math.DG/0305124 · arXiv
  6. Candelas, P., Horowitz, G., Strominger, A., Witten, E.: Vacuum configurations for superstrings. Nucl. Phys. B 258, 46–74 (1985) · DOI
  7. Cao, H.-D., Hamilton, R.S., Ilmanen, T.: Gaussian densities and stability for some Ricci solitons. math.DG/0404165 · arXiv
  8. Cheeger, J., Gromoll, D.: The splitting theorem for manifolds of non-negative Ricci curvature. J. Differ. Geom. 6, 119–128 (1971) · DOI
  9. Dai, X.: A Positive Mass Theorem for Sapces with Asymptotic SUSY Compactifcation. Commun. Math. Phys. 244, 335–345 (2004) · DOI
  10. do Carmo, M.: Riemannian Geometry. Birkhäuser 1992 · DOI
  11. Fischer, A., Marsden, J.: Linearization stability of nonlinear partial differential equations. In: Differential geometry (Proc. Symp. Pure Math., vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2, pp. 219–263. Providence, R.I.: Amer. Math. Soc. 1975 · DOI
  12. Futaki, A.: Scalar-flat closed manifolds not admitting positive scalar curvature metrics. Invent. Math. 112, 23–29 (1993) · DOI
  13. Gromov, M., Lawson Jr., H.B.: The classification of simply connected manifolds of positive scalar curvature. Ann. Math. 111, 423–434 (1980) · DOI
  14. Guenther, C., Isenberg, J., Knopf, D.: Stability of the Ricci flow at Ricci-flat metrics. Commun. Anal. Geom. 10, 741–777 (2002) · DOI
  15. Hertog, T., Horowitz, G., Maeda, K.: Negative energy density in Calabi-Yau compactifications. JHEP 0305, 060 (2003). hep-th/0304199 · DOI · Paper page
  16. Hitchin, N.: Harmonic spinors. Adv. Math. 14, 1–55 (1974) · DOI
  17. Hitchin, N.: Compact four-dimensional Einstein manifolds. J. Differ. Geom. 9, 435–441 (1974) · DOI
  18. Joyce, D.: Compact manifolds with special holonomy. Oxford: Oxford Univ. Press 2000 · DOI
  19. Kazdan, J.L., Warner, F.W.: Prescribing curvatures. In: Differential geometry (Proc. Symp. Pure Math., vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2, pp. 309–319. Providence, R.I.: Amer. Math. Soc. 1975 · DOI
  20. Koiso, N.: Rigidity and stability of Einstein metrics. The case of compact symmetric spaces. Osaka J. Math. 17, 51–73 (1980)
  21. Lawson Jr., H.B., Michelsohn, M.-L.: Spin geometry. Princeton, NJ: Princeton University Press 1989
  22. Lichnerowicz, A.: Spineurs harmonique. C. R. Acad. Sci., Paris, Sér. A-B 257, 7–9 (1963)
  23. Milnor, J.: A note on curvature and fundamental group. J. Differ. Geom. 2, 1–7 (1968) · DOI
  24. Morgan, J.: The Seiberg-Witten equations and applications to the topology of smooth four-manifolds. Princeton, NJ: Princeton Univ. Press 1996 · DOI
  25. Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. math.DG/0211159 · arXiv
  26. Schoen, R.M.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom. 20, 479–495 (1984) · DOI
  27. Schoen, R.M.: Variational theory for the total scalar curvature functional for Riemannian metrics and related topics. In: Topics in calculus of variations (Montecatini Terme, 1987), pp. 120–154. Berlin: Springer 1989 · DOI
  28. Schoen, R.M., Yau, S.T.: On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys. 65, 45–76 (1979) · DOI · Paper page
  29. Schoen, R.M., Yau, S.T.: On the structure of manifolds with posiitve scalar curvature. Manuscr. Math. 28, 159–183 (1979) · DOI
  30. Stolz, S.: Simply connected manifolds of positive scalar curvature. Ann. Math. 136, 511–540 (1992) · DOI
  31. Todorov, A.: The Weil-Petersson geometry of the moduli space of SU(n≥3) (Calabi-Yau) manifolds. I. Commun. Math. Phys. 126, 325–346 (1989) · DOI · Paper page
  32. Wang, M.: Parallel spinors and parallel forms. Ann. Global Anal. Geom. 7, 59–68 (1989) · DOI
  33. Wang, M.: Preserving parallel spinors under metric deformations. Indiana Univ. Math. J. 40, 815–844 (1991) · DOI
  34. Wei, G.: Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups. Bull. Am. Math. Soc., New Ser. 19, 311–313 (1988) · DOI
  35. Witten, E.: A new proof of the positive energy theorem. Commun. Math. Phys. 80, 381–402 (1981) · DOI · Paper page
  36. Yau, S.T.: Calabi’s conjecture and some new results in algebraic geometry. Proc. Natl. Acad. Sci. USA 74, 1798–1799 (1977) · DOI
  37. Yau, S.T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I. Commun. Pure Appl. Math. 31, 339–411 (1978) · DOI

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Metadata

Authors
Dai, X., Wang, X., & Wei, G.
Venue
Inventiones mathematicae
Publisher
Springer Science and Business Media LLC
Published
2005-03-01
Volume
161
Issue
1
Pages
151-176
ISSN
  • 0020-9910
  • 1432-1297
DOI
10.1007/s00222-004-0424-x
Cited by
45
References
2
Language
en
Licence
www.springer.com/tdm (tdm)

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Dai, X., Wang, X., & Wei, G. (2005). On the stability of Riemannian manifold with parallel spinors. Inventiones mathematicae. https://doi.org/10.1007/s00222-004-0424-x

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