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Laplacian with a potential

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Part of the Lecture Notes in Mathematics book series (LNM,volume 838)

Keywords

  • Riemannian Manifold
  • Sectional Curvature
  • Integral Formula
  • Grad Versus
  • Curvature Vector

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References

  1. K. Benko, M. Kothe, K.-D. Semmler, U. Simon, Eigenvalues of the Laplacian and curvature, Colloquium math., to appear.

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  2. M. Berger, P. Gauduchon, E. Mazet, Le spectra d’une variété riemannienne, Lecture Notes in Mathematics 194 (1971), Springer, Berlin-Heidelberg-New York.

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  3. L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press 19604.

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  4. M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. math. Soc. Japan 14 (1962), 333–340.

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  5. E. Schrödinger, Abhandlung zur Wellenmechanik, Johann Ambrosius Barth, Leipzig 1927.

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  6. U. Simon, Curvature bounds for the spectrum of closed Einstein spaces, Canadian J. Math. Z. 153 (1977), 23–27.

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  7. U. Simon, Submanifolds with parallel mean curvature vector and the curvature of minimal submanifolds of spheres, Archiv Math. 29 (1977), 106–112.

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  8. S. Tanno, Some differential equations on Riemannian manifolds, Colloquium math., to appear.

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© 1981 Springer-Verlag

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Barthel, D., Kümritz, R. (1981). Laplacian with a potential. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088838

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  • DOI: https://doi.org/10.1007/BFb0088838

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10285-4

  • Online ISBN: 978-3-540-38419-9

  • eBook Packages: Springer Book Archive