Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NOTE ON THE EIGENFUNCTIONS OF THE LAPLACIAN FOR A TWISTED HOLOMORPHIC PRODUCT

  • Peter B.Gilkey (Mathematics Department, University of Oregon) ;
  • Park, Jeong-Hyeong (Department of Mathematics, Honam University)
  • Published : 1997.04.01
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Abstract

Let $Z = X \times Y$ where X and Y are complex manifolds. We suppose that projection $\pi$ on the second factor is a Riemannian submersion, that TX is perpendicular to TY, and that the metrics on Z and on Y are Hermetian; we do not assume Z is a Riemannian product. We study when the pull-back of an eigenfunction of the complex Laplacian on Y is an eigenfunction of the complex Laplacian on Z.

Keywords

References

  1. Invariance Theory, the Heat Equation, and the Atiyah-Singer Index theorem (2nd edition), ISBN 0-8493-7874-4 P. B. Gilkey
  2. Illinois J. Math v.40 Riemannian submersions which preserve the eigne forms of the Laplacian P. B. Gilkey;. H. Park
  3. Bull. Korean Math. Soc. v.27 The Laplace-Beltrami operator and Riemannian submersion with minimal and not totally geodesic fibers J. H. Park
  4. Honam Mathermatical Journal v.16 A note on eigenfunctions of the Laplacian of warped products J. H. Park
  5. Kyungpook Math. J. v.35 A note on the eigenfunctions of the Laplacian for twisted products J. H. Park