The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
Urakawa, Hajime
Compositio Mathematica, Tome 60 (1986), p. 57-71 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1986-01-01
@article{CM_1986__59_1_57_0,
     author = {Urakawa, Hajime},
     title = {The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold},
     journal = {Compositio Mathematica},
     volume = {60},
     year = {1986},
     pages = {57-71},
     mrnumber = {850121},
     zbl = {0615.53040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1986__59_1_57_0}
}

Urakawa, Hajime. The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold. Compositio Mathematica, Tome 60 (1986) pp. 57-71. http://gdmltest.u-ga.fr/item/CM_1986__59_1_57_0/

[AW] S. Aloff and N.R. Wallach: An infinite family of distinct 7-manifolds admitting positively curved Riemannian metrics. Bull. Amer. Math. Soc., 81 (1975) 93-97. | MR 370624 | Zbl 0362.53033

[BU] S. Bando and H. Urakawa: Generic properties of the eigenvalues of the Laplacian for compact Riemannian manifolds. Tohoku Math. Jour., 35 (1983) 155-172. | MR 699924

[BBG] P. Berard, G. Besson and S. Gallot: Sur une inegalite isoperimetrique qui generalise celle de Paul Levy-Gromov. Invent. Math., (1985). | Zbl 0571.53027

[BB 1] L. Btrard Bergery: Sur certaines fibrations d'espaces homogenes riemanniens. Compos. Math., 30 (1975), 43-61. | Numdam | MR 370432 | Zbl 0304.53036

[BB 2] L. Bérard Bergery: Les variétés riemanniennes homogènes simplement con- nexes de dimension impaire a courbure strictement positive. J. Math. pures appl., 55 (1976) 47-68. | MR 417987 | Zbl 0289.53037

[BBB] L. Bérard Bergery and J.P. Bourguignon: Laplacians and Riemannian submersions with totally geodesic fibers. Illinois J. Math., 26 (1982) 181-200. | MR 650387 | Zbl 0483.58021

[B] M. Berger: Les variétés riemanniennes homogenes normales simplement connexes a courbure strictement positive. Ann. Scuol. Norm. Sup. Pisa, 15 (1961) 179-246. | Numdam | MR 133083 | Zbl 0101.14201

[Bo] N. Bourbaki: Groupes et algèbres de Lie, Chap. 4, 5 et 6, Paris: Herman (1968). | MR 240238 | Zbl 0483.22001

[CW] R.S. Cahn and J.A. Wolf: Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one. Comment. Math. Helv., 51 (1976) 1-21. | MR 397801 | Zbl 0327.43013

[C] C.B. Croke: An eigenvalue pinching problem. Invent. Math., 68 (1982) 253-256. | MR 666162 | Zbl 0505.53018

[H] H.M. Huang: Some remarks on the pinching problems. Bull. Inst. Math. Acad. Sinica, 9 (1981) 321-340. | MR 625725 | Zbl 0477.53043

[He] S. Helgason: Differential geometry and symmetric spaces, New York: Academic Press (1962). | MR 145455 | Zbl 0111.18101

[KN] S. Kobayashi and K. Nomizu: Foundations of differential geometry, II, New York: Interscience (1969). | MR 238225 | Zbl 0175.48504

[LT] P. Li and A.E. Treibergs: Pinching theorem for the first eigenvalue on positively curved four-manifolds. Invent. Math., 66 (1982) 35-38. | MR 652644 | Zbl 0496.53032

[LZ] P. Li and J.Q. Zhong: Pinching theorem for the first eigenvalue on positively curved manifolds. Invent. Math., 65 (1981) 221-225. | MR 641128 | Zbl 0496.53031

[MU] H. Muto and H. Urakawa: On the least positive eigenvalue of Laplacian for compact homogeneous spaces. Osaka J. Math., 17 (1980) 471-484. | MR 587767 | Zbl 0446.53037

[N 1] T. Nagano: On the minimum eigenvalues of the Laplacians in Riemannian manifolds, Sci. Papers Coll. Gen. Ed. Univ. Tokyo, 11 (1961) 177-182. | MR 144283 | Zbl 0134.31005

[N 2] T. Nagano: Stability of harmonic maps between symmetric spaces, Proc. Tulane, Lecture Note in Math. 949, Springer Verlag: New York (1982), 130-137. | MR 673587 | Zbl 0507.58019

[Sm] R.T. Smith: The second variation formula for harmonic mappings. Proc. Amer. Math. Soc., 47 (1975) 229-236. | MR 375386 | Zbl 0303.58008

[Su] M. Sugiura: Representation of compact groups realized by spherical functions on symmetric spaces. Proc. Japan Acad., 38 (1962) 111-113. | MR 142689 | Zbl 0134.26901

[T] M. Takeuchi: Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku Math. Jour. 36 (1984) 293-314. | MR 742600 | Zbl 0528.53047

[TK] M. Takeuchi And S. Kobayashi: Minimal imbedding of R-spaces. J. Diff. Geom., 2 (1968) 203-215. | MR 239007 | Zbl 0165.24901

[U] H. Urakawa: Numerical computations of the spectra of the Laplacian on 7-dimensional homogeneous manifolds SU(3)/T(k, l). SIAM J. Math. Anal., 15 (1984) 979-987. | MR 755857 | Zbl 0548.53045

[W] N.R. Wallach: Compact homogeneous Riemannian manifolds with strictly positive curvature. Ann. Math., 96 (1972) 277-295. | MR 307122 | Zbl 0261.53033

[Wr] G. Warner: Harmonic analysis on semi-simple Lie groups, I, Berlin, Heidelberg, New York: Springer Verlag (1972). | MR 498999 | Zbl 0265.22020