The second variation formula for harmonic mappings
HTML articles powered by AMS MathViewer
- by R. T. Smith
- Proc. Amer. Math. Soc. 47 (1975), 229-236
- DOI: https://doi.org/10.1090/S0002-9939-1975-0375386-2
- PDF | Request permission
Abstract:
The formula of the title is computed, and is used to calculate the index and nullity in several cases.References
- K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. MR 0062505
- James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. MR 164306, DOI 10.2307/2373037
- Halldór I. Elĭasson, Geometry of manifolds of maps, J. Differential Geometry 1 (1967), 169–194. MR 226681 —, Variational integrals in fibre bundles, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R. I., 1970, pp. 67-89. MR 42 #2507.
- Philip Hartman, On homotopic harmonic maps, Canadian J. Math. 19 (1967), 673–687. MR 214004, DOI 10.4153/CJM-1967-062-6
- Robert Hermann, The second variation for variational problems in canonical form, Bull. Amer. Math. Soc. 71 (1965), 145–148. MR 172216, DOI 10.1090/S0002-9904-1965-11263-0
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0238225 A. Lichnérowicz, Géométrie des groupes de transformations, Travaux et Recherches Mathématiques, III, Dunod, Paris, 1958. MR 23 #A1329.
- André Lichnerowicz, Applications harmoniques et variétés kähleriennes, Symposia Mathematica, Vol. III (INDAM, Rome, 1968/69) Academic Press, London, 1968/1969, pp. 341–402 (French). MR 0262993
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
- Tadashi Nagano, On the minimum eigenvalues of the Laplacians in Riemannian manifolds, Sci. Papers College Gen. Ed. Univ. Tokyo 11 (1961), 177–182. MR 144283
- Tadashi Nagano, On conformal transformations of Riemannian spaces, J. Math. Soc. Japan 10 (1958), 79–93. MR 110991, DOI 10.2969/jmsj/01010079
- Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299–340. MR 158410, DOI 10.1016/0040-9383(63)90013-2
- S. Smale, On the Morse index theorem, J. Math. Mech. 14 (1965), 1049–1055. MR 0182027, DOI 10.1111/j.1467-9876.1965.tb00656.x R. T. Smith, Thesis, Warwick University, 1972.
- Kentaro Yano and Tadashi Nagano, On geodesic vector fields in a compact orientable Riemannian space, Comment. Math. Helv. 35 (1961), 55–64. MR 124854, DOI 10.1007/BF02567005
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 229-236
- MSC: Primary 58E15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0375386-2
- MathSciNet review: 0375386