¹Yancheng Institute of Technology, Yancheng, China. Peking University, Peking, China. Email: chfxue@gmail.com
²Peking University, Peking, China. Email: tanwch@mech.pku.edu.cn

In this paper, some basic properties of the cohomology solution on ring surfaces of genus g are presented, and the theorem of Dolbeault and the theorem of Serre for the operator are obtained. The index theorem on such ring surfaces of genus g is also discussed.

Key words: Ring surface, cohomology, genus, index.

En este artículo se presentan algunas propiedades básicas de la solución cohomológica para superficies sobre anillos de género g y se obtienen los teoremas de Dolbeault y Serre para el operador . Se discute el teorema del índice para tales superficies.

Palabras clave: Superficie sobre anillos, cohomología, género, índice.

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References

[1] Ahlfors, L. & Sario, L., Riemann Surfaces, Princeton University Press, New Jersey, United States, 1960.         [ Links ]

[2] Farkas, H. & Kra, I., Riemann Surfaces, Springer, New York, United States, 1980.         [ Links ]

[3] Hou, B., Differential Geometry Used by Physicists, 2 edn, Science Press, Beijing, China, 2004.         [ Links ]

[4] Kobayashi, S. & Nomizu, K., Foundations of Differential Geometry, Vol. II, Interscience, New York, United States, 1969.         [ Links ]

[5] Lv, Y. & Zhang, X., Riemann surfaces, Science Press, Beijing, China, 1991.         [ Links ]

[6] Su, J., Topology of Manifold, 2 edn, Wuhan University Press, Wuhan, China, 2005.         [ Links ]

[7] Wu, H., Lv, Y. & Chen, Z., Introduction of Riemann Surfaces, Science Press, Beijing, China, 1981.         [ Links ]

[8] Xiao, G., The Fibrations of Algebraic Surfaces, Shanghai Scientific and Technical Publishers, Shanghai, China, 1992.         [ Links ]

[9] Xue, C. & Tan, W., The solutions of covariant derivative equations of cross section in associated bundles. Nonlinear Analysis: Theory, Methods and Applications (in press, doi:10.1016/j.na.2007.03.033).         [ Links ]

[10] Zhou, B., Cohomology Algebraic, Science Press, Beijing, China, 1988.         [ Links ]

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