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Tong, Y. L.; Wang, S. P.

Harmonic forms dual to geodesic cycles in quotients of SU(p,1). (English) Zbl 0466.58004

Math. Ann. 258, 289-318 (1982).
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Cited in 5 Reviews
Cited in 5 Documents

MSC:

58A14 Hodge theory in global analysis
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q99 Complex manifolds
32C37 Duality theorems for analytic spaces

Keywords:

differential forms which are Poincare dual to geodesic cycles in complex hyperbolic manifolds; action of Laplacian; harmonic forms
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Full Text: DOI EuDML

References:

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[2] Bishop, R.L., Crittenden, R.J.: Geometry of manifolds, New York: Academic Press 1964 · Zbl 0132.16003
[3] Bott, R., Chern, S.S.: Some formulas related to complex transgression. Essays on Topology and Related Topics. Berlin, Heidelberg, New York: Springer 1970 · Zbl 0203.54202
[4] Gaffney, M.: Asymptotic distributions assocaited with the Laplacian for forms. Comm. Pure Applied Math.11, 535-545 (1958) · Zbl 0102.09604 · doi:10.1002/cpa.3160110405
[5] Griffiths, P.A.: Some results on algebraic cycles on algebraic manifolds. Algebraic geometry, Bombay Colloquium 1968. Oxford: Oxford University Press 1969 · Zbl 0188.24801
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[10] Kudla, S., Millson, J.: Harmonic differentials and closed geodesics on a Riemann surface. Invent. Math.54, 193-211 (1979) · Zbl 0429.30038 · doi:10.1007/BF01390229
[11] Kudla, S., Millson, J.: Geodesic cycles and the Weil representation. I. Quotients of the hyperbolic space and Siegel modular forms (preprint) · Zbl 0495.10016
[12] Oda, T.: On modular forms associated with indefinite quadratic forms of signature (2,n-2). Math. Ann.231, 97-144 (1977) · doi:10.1007/BF01361138
[13] Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagoya Math. J.58, 83-126 (1975) · Zbl 0316.10016
[14] Tong, Y.L.: Weighted intersection numbers on Hilbert modular surfaces. Compositio Math.38, 299-310 (1979) · Zbl 0409.10017
[15] Weil, A.: Varieties K?hleriennes. Paris: Hermann 1971
[16] Wells, R.O.: Differential analysis on complex manifolds. Englewood Cliffs, N.J.: Prentice Hall 1973 · Zbl 0262.32005
[17] Zagier, D.: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, Modular functions of one variable VI, Bonn, Lecture Notes in Mathematics, Vol. 627. Berlin, Heidelberg, New York: Springer 1976
[18] Kudla, S.: On certain arithmetic automorphic forms for SU (1,q). Invent. Math.52, 1-25 (1979) · Zbl 0408.10016 · doi:10.1007/BF01389855
[19] Kudla, S. Millson, J.: The Poincar? dual of a geodesic algebraic curve in a quotient of the 2-ball (preprint) · Zbl 0506.32013
[20] Tong. Y.L., Wang, S.P.: Theta functions defined by geodesic cycles in quotients of SU (p, 1) (in preparation) · Zbl 0506.10024
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