The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
Compositio Mathematica, Volume 59 (1986) no. 1, pp. 57-71.
@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},
     pages = {57--71},
     publisher = {Martinus Nijhoff Publishers},
     volume = {59},
     number = {1},
     year = {1986},
     zbl = {0615.53040},
     mrnumber = {850121},
     language = {en},
     url = {http://www.numdam.org/item/CM_1986__59_1_57_0/}
}
TY  - JOUR
AU  - Urakawa, Hajime
TI  - The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
JO  - Compositio Mathematica
PY  - 1986
DA  - 1986///
SP  - 57
EP  - 71
VL  - 59
IS  - 1
PB  - Martinus Nijhoff Publishers
UR  - http://www.numdam.org/item/CM_1986__59_1_57_0/
UR  - https://zbmath.org/?q=an%3A0615.53040
UR  - https://www.ams.org/mathscinet-getitem?mr=850121
LA  - en
ID  - CM_1986__59_1_57_0
ER  - 
%0 Journal Article
%A Urakawa, Hajime
%T The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
%J Compositio Mathematica
%D 1986
%P 57-71
%V 59
%N 1
%I Martinus Nijhoff Publishers
%G en
%F CM_1986__59_1_57_0
Urakawa, Hajime. The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold. Compositio Mathematica, Volume 59 (1986) no. 1, pp. 57-71. http://www.numdam.org/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 | Zbl

[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

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

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

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

[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 | Zbl

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

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