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A curvature obstruction to covering deformations of connections by metric deformations

Author: Paul E. Ehrlich
Journal: Proc. Amer. Math. Soc. 52 (1975), 337-342
MSC: Primary 53C20
MathSciNet review: 0383293
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Abstract: A curvature obstruction to covering a deformation of connections of a Levi-Civita connection of a Riemannian metric by a metric deformation is derived and used to study deformations of connections related to the deformation of connections arising from a conformal deformation of a Riemannian metric.

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  • [1] T. Aubin, Métriques riemannienes et courbure, J. Differential Geometry 4 (1970), 383-424. MR 43 #5452. MR 0279731 (43:5452)
  • [2] M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379-392. MR 42 #993. MR 0266084 (42:993)
  • [3] J.-P. Bourguignon, Transformations infinitésimales conformes fermées des variétés riemannienes connexes complètes, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1593-A1596. MR 42 #5192. MR 0270302 (42:5192)
  • [4] P. E. Ehrlich, Local convex deformations of Ricci and sectional curvature on compact Riemannian manifolds, Proc. Sympos. Pure Math., vol. 27, Part I, Amer. Math. Soc., Providence, R. I., 1975, 69-72. MR 0383315 (52:4196)
  • [5] N. J. Hicks, Notes on differential geometry, Van Nostrand Math. Studies, no. 3, Van Nostrand, Princeton, N. J., 1965. MR 31 #3936. MR 0179691 (31:3936)
  • [6] M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247-258. MR 46 #2601. MR 0303464 (46:2601)
  • [7] K. Yano, Integral formulas in Riemannian geometry, Pure and Appl. Math., no. 1, Dekker, New York, 1970. MR 44 #2174. MR 0284950 (44:2174)

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Article copyright: © Copyright 1975 American Mathematical Society

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