×

zbMATH — the first resource for mathematics

The second variation formula for harmonic mappings. (English) Zbl 0303.58008

MSC:
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
53C20 Global Riemannian geometry, including pinching
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. · Zbl 0051.39402
[2] James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109 – 160. · Zbl 0122.40102 · doi:10.2307/2373037 · doi.org
[3] Halldór I. Elĭasson, Geometry of manifolds of maps, J. Differential Geometry 1 (1967), 169 – 194.
[4] -, Variational integrals in fibre bundles, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R. I., 1970, pp. 67-89. MR 42 #2507.
[5] Philip Hartman, On homotopic harmonic maps, Canad. J. Math. 19 (1967), 673 – 687. · Zbl 0148.42404 · doi:10.4153/CJM-1967-062-6 · doi.org
[6] Robert Hermann, The second variation for variational problems in canonical form, Bull. Amer. Math. Soc. 71 (1965), 145 – 148. · Zbl 0141.10702
[7] 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. · Zbl 0091.34802
[8] A. Lichnérowicz, Géométrie des groupes de transformations, Travaux et Recherches Mathématiques, III, Dunod, Paris, 1958. MR 23 #A1329. · Zbl 0096.16001
[9] André Lichnerowicz, Applications harmoniques et variétés kähleriennes, Symposia Mathematica, Vol. III (INDAM, Rome, 1968/69) Academic Press, London, 1968/1969, pp. 341 – 402 (French).
[10] J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. · Zbl 0108.10401
[11] Tadashi Nagano, On the minimum eigenvalues of the Laplacians in Riemannian manifolds., Sci. Papers Coll. Gen. Ed. Univ. Tokyo 11 (1961), 177 – 182. · Zbl 0134.31005
[12] Tadashi Nagano, On conformal transformations of Riemannian spaces, J. Math. Soc. Japan 10 (1958), 79 – 93. · Zbl 0081.15804 · doi:10.2969/jmsj/01010079 · doi.org
[13] Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299 – 340. · Zbl 0122.10702 · doi:10.1016/0040-9383(63)90013-2 · doi.org
[14] S. Smale, On the Morse index theorem, J. Math. Mech. 14 (1965), 1049 – 1055. · Zbl 0166.36102
[15] R. T. Smith, Thesis, Warwick University, 1972.
[16] Kentaro Yano and Tadashi Nagano, On geodesic vector fields in a compact orientable Riemannian space., Comment. Math. Helv. 35 (1961), 55 – 64. · Zbl 0100.35904 · doi:10.1007/BF02567005 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.