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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. v.41 n.2 Bogotá jul./dez. 2007
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.
2000 Mathematics Subject Classification: 53C21, 53C42.
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.
Texto completo disponible en PDF
References
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[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 ]
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[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 ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{XueTan07,
AUTHOR = {Changfeng Xue and Wenchang Tan},
TITLE = {{The cohomology solution and the index theorem on ring surfaces of genus g}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2007},
volume = {41},
number = {2},
pages = {371-380}
}