底空间为对称域乘积的Hartogs域的度量等价

王安, 李志强

数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 871-888.

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PDF(535 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 871-888. DOI: 10.12386/A2013sxxb0084
论文

底空间为对称域乘积的Hartogs域的度量等价

    王安, 李志强
作者信息 +

Metric Equivalence of Hartogs Domains Whose Base Space Is a Product of Symmetric Domain

    An WANG, Zhi Qiang LI
Author information +
文章历史 +

摘要

研究一类非齐性Hartogs域上经典度量的等价问题.首先证明了Bergman-度量和Einstein-Kähler度量在这类域上等价;其次,当域的参数满足+<1 时,此类域上Bergman 度量, Carathéodary 度量, Kobayashi度量和Einstein-Kähler 度 量是等价的.

Abstract

We study the equivalent problem of the classical metric on a class of nonhomogeneous Hartogs domain. Firstly, it is proved that the equivalence between the Bergman and the Einstein-Kähler metrics on these domains; Secondly, it is shown that the Bergman metric, the Carathéodary metric, the Kobayashi metric and the Einstein- Kähler metric are equivalent, when parameters of the domain satisfy + < 1.

关键词

Bergman度量 / Einstein-Kähler度量 / Kobayashi度量 / Carathéodary度量

Key words

Bergman metric / Einstein-Kähler metric / Kobayashi metric / Carathéodary

引用本文

导出引用
王安, 李志强. 底空间为对称域乘积的Hartogs域的度量等价. 数学学报, 2013, 56(6): 871-888 https://doi.org/10.12386/A2013sxxb0084
An WANG, Zhi Qiang LI. Metric Equivalence of Hartogs Domains Whose Base Space Is a Product of Symmetric Domain. Acta Mathematica Sinica, Chinese Series, 2013, 56(6): 871-888 https://doi.org/10.12386/A2013sxxb0084

参考文献

[1] Diederich K., Fornaess J. E., Comparison of the Kobayashi and the Bergman metrics, Annals of Mathematics, 1980, 254: 257-262.

[2] Dineen S., The Schwarz Lemma, Clarendon Press, Oxford, 1989.

[3] Hahn K. T., Inequality between the Bergman metric and Carathéodory differential metric, Proc. Amer. Math. Soc., 1978, 68: 193-194.

[4] Hahn K. T., Pflug P., The Kobayashi and Bergman metrics on generalized Thullen domains, Proc. Amer. Math. Soc., 1988, 104: 207-214.

[5] Heins M., On a class of conformal metrics, Nagoya Math. J., 1962, 21: 1-60.

[6] Kobayashi S., Intrinsic sistances, measures and geometric function theory, Bull. Amer. Math. Soc., 1976, 82: 357-416.

[7] Kuang J. C., Applied Inequalities (3rd ed.), Shandong Sci. and Technology Press, 2004 (in Chinese).

[8] Lempert L., Holomorphic reretracs and intrinsic metrics in convex domains, Anal. Math., 1982, 8: 257-261.

[9] Li H. T., Su J. B., The convexity and Kobayashi metric on the super-cartan domain of the third type, Mathematics in Practice and Theory, 2010, 40(8): 172-178 (in Chinese).

[10] Lin P., Yin W. P., The comparison theorem on super-Cartan domains of the fourth type, Adv. Math. of China, 2003, 32(6): 739-750 (in Chinese).

[11] Liu K. F., Sun X. F., Yau S. T., Canonical metrics on the moduli space of Riemann surface I, J. Differential Geom., 2004, 68(3): 571-637.

[12] Liu K. F., Sun X. F., Yau S. T., Canonical metrics on the moduli space of Riemann surface Ⅱ, J. Differential Geom., 2005, 69(1): 163-216.

[13] Liu K. F., Sun X. F., Yau S. T., Geometric aspects of the moduli space of Riemann surfaces, Sci. in China, Ser. A, 2005, 48(Supp): 97-122.

[14] Lu Q. K., The Classical Manifolds and the Classical Domains, Shanghai Sci. and Technical Press, Shanghai, 1963 (in Chinese).

[15] Su J. B., The invariant metrics on the super-cartan domain of the first type, Adv. Math. of China, 2007, 36(6): 686-692.

[16] Wang A., Liu Y. L., Zeroes of the Bergman kernels on some new Hartogs domains, Chinese Quarterly J. of Mathematics, 2011, 26(3): 325-334.

[17] Yau S. T., A general Schwarz lemma for Kähler manifolds, Amer. J. Math., 1978, 100(1): 197-203.

[18] Yau S. T., Schoen R., Lectures on Differential Geometry, Higher Education Press, Beijin, 2004 (in Chinese).

[19] Ye W. W., Complete Einstein-Kähler metrics of a class of non-homogeneous domain, Master Dissertation of Capital Normal University, 2011 (in Chinese).

[20] Yin W. P., The comparison theorem for the Bergman and Kobayashi metrics on certain pseudoconvex domains, Complex Variables, 1997, 34: 351-373.

[21] Yin W. P., Wang A., The equivalence on classical metrics, Sci. China, Ser. A, 2007, 50(2): 183-200.

[22] Yin W. P., Wang A., Zhao X. X., The comparison theorem for the Bergman and Kobayashi metrics on Cartan-Hartogs domains of the first type, Sci. China, Ser. A, 2001, 44(5): 587-598.

[23] Yin W. P., Zhao X. X., The comparison theorem on Cartan-Hartogs domain of the third type, Complex Variables, 2002, 47(3): 183-201.

[24] Yin W. P., Zhang L. Y., Equivalence of the Einstein-Kähler metric and Bergman metric on Cartan-Hartogs domain, Adv. Math. of China, 2008, 37(4): 437-450.

[25] Yin W. P., Zhang L. Y., Equivalence between Kähler-Einstein and Bergman metrics, Chinese Annals of Mathematics, 2007, 28A(4): 545-556 (in Chinese).

[26] Zhao X. X., Ding L., Yin W. P., The comparison theorem on Cartan-Hartogs domain of the second type, Progress in Natural Sci., 2004, 14(2): 105-112.

[27] Zhao X. X., Lin P., The equivalence between Bergman metric and Einstein-Kähler metric on the Cartan-Hartogs domain of the fourth type, Chinese Quarterly J. of Mathematics, 2008, 23(3): 317-324.

基金

国家自然科学基金资助项目(11071171);北京自然科学基金资助项目(1122010)

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