On the construction of some complete metrics with exceptional holonomy

Duke Mathematical Journal - Tập 58 Số 3 - 1989
Robert L. Bryant, Simon Salamon

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Tài liệu tham khảo

[A] D. V. Alekseevskii, <i>Riemannian spaces with exceptional holonomy groups</i>, Functional Anal. Appl. <b>2</b> (1968), 97–105.

[AHS] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, <i>Self-duality in four-dimensional Riemannian geometry</i>, Proc. Roy. Soc. London Ser. A <b>362</b> (1978), no. 1711, 425–461.

[B] M. Berger, <i>Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés riemanniennes</i>, Bull. Soc. Math. France <b>83</b> (1955), 279–330.

[BB] L. Bérard-Bergery, <i>Sur de nouvelles variétés riemanniennes d'Einstein</i>, Institut Élie Cartan, 6, Inst. Élie Cartan, vol. 6, Univ. Nancy, Nancy, 1982, pp. 1–60.

[Be] A. L. Besse, <i>Minimal Lagrangian submanifolds of Kähler-Einstein manifolds</i>, Lecture Notes in Math., vol. 1255, Springer, Berlin, 1987.

[Bo] E. Bonan, <i>Sur les variétés riemanniennes à groupe d'holonomie $G_2$ ou $\mathrm{Spin}(7)$</i>, C. R. Acad. Sci. Paris <b>262</b> (1966), 127–129.

[Br] R. L. Bryant, <i>Metrics with exceptional holonomy</i>, Ann. of Math. (2) <b>126</b> (1987), no. 3, 525–576.

[C1] E. Calabi, <i>Construction and properties of some $6$-dimensional almost complex manifolds</i>, Trans. Amer. Math. Soc. <b>87</b> (1958), 407–438.

[C2] E. Calabi, <i>Métriques kählériennes et fibrés holomorphes</i>, Ann. Sci. École Norm. Sup. (4) <b>12</b> (1979), no. 2, 269–294.

[ES] J. Eells and S. Salamon, <i>Twistorial construction of harmonic maps of surfaces into four-manifolds</i>, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) <b>12</b> (1985), no. 4, 589–640 (1986).

[F] M. Fernandez, <i>A classification of Riemannian manifolds with structure group ${\rm Spin}(7)$</i>, Ann. Mat. Pura Appl. (4) <b>143</b> (1986), 101–122.

[GL] K. Galicki and H. B. Lawson, <i>Quaternionic-Kähler manifolds and Marsden-Weinstein type reduction</i>, preprint.

[Gr] A. Gray, <i>Weak holonomy groups</i>, Math. Z. <b>123</b> (1971), 290–300.

[H] N. J. Hitchin, <i>Kählerian twistor spaces</i>, Proc. London Math. Soc. (3) <b>43</b> (1981), no. 1, 133–150.

[HL] R. Harvey and H. B. Lawson, <i>Calibrated geometries</i>, Acta Math. <b>148</b> (1982), 47–157.

[M] S. Marchiafava, <i>Alcune osservazioni riguardanti i gruppi di Lie $G_2 e \mathrm{Spin}(7)$, candidati a gruppi di olonomia</i>, Ann. Mat. Pura appl. <b>129</b> (1981), 247–264.

[PP] D. N. Page and C. N. Pope, <i>Einstein metrics on quaternionic line bundles</i>, Classical Quantum Gravity <b>3</b> (1986), no. 2, 249–259.