@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},
year = {1986},
publisher = {Martinus Nijhoff Publishers},
volume = {59},
number = {1},
mrnumber = {850121},
zbl = {0615.53040},
language = {en},
url = {https://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 SP - 57 EP - 71 VL - 59 IS - 1 PB - Martinus Nijhoff Publishers UR - https://www.numdam.org/item/CM_1986__59_1_57_0/ LA - en ID - CM_1986__59_1_57_0 ER -
Urakawa, Hajime. The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold. Compositio Mathematica, Tome 59 (1986) no. 1, pp. 57-71. https://www.numdam.org/item/CM_1986__59_1_57_0/
[AW] and : An infinite family of distinct 7-manifolds admitting positively curved Riemannian metrics. Bull. Amer. Math. Soc., 81 (1975) 93-97. | Zbl | MR
[BU] and : Generic properties of the eigenvalues of the Laplacian for compact Riemannian manifolds. Tohoku Math. Jour., 35 (1983) 155-172. | MR
[BBG] , and : Sur une inegalite isoperimetrique qui generalise celle de Paul Levy-Gromov. Invent. Math., (1985). | Zbl
[BB 1] : Sur certaines fibrations d'espaces homogenes riemanniens. Compos. Math., 30 (1975), 43-61. | Zbl | MR | Numdam
[BB 2] : Les variétés riemanniennes homogènes simplement con- nexes de dimension impaire a courbure strictement positive. J. Math. pures appl., 55 (1976) 47-68. | Zbl | MR
[BBB] and : Laplacians and Riemannian submersions with totally geodesic fibers. Illinois J. Math., 26 (1982) 181-200. | Zbl | MR
[B] : Les variétés riemanniennes homogenes normales simplement connexes a courbure strictement positive. Ann. Scuol. Norm. Sup. Pisa, 15 (1961) 179-246. | Zbl | MR | Numdam
[Bo] : Groupes et algèbres de Lie, Chap. 4, 5 et 6, Paris: Herman (1968). | Zbl | MR
[CW] and : Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one. Comment. Math. Helv., 51 (1976) 1-21. | Zbl | MR
[C] : An eigenvalue pinching problem. Invent. Math., 68 (1982) 253-256. | Zbl | MR | EuDML
[H] : Some remarks on the pinching problems. Bull. Inst. Math. Acad. Sinica, 9 (1981) 321-340. | Zbl | MR
[He] : Differential geometry and symmetric spaces, New York: Academic Press (1962). | Zbl | MR
[KN] and : Foundations of differential geometry, II, New York: Interscience (1969). | Zbl | MR
[LT] and : Pinching theorem for the first eigenvalue on positively curved four-manifolds. Invent. Math., 66 (1982) 35-38. | Zbl | MR | EuDML
[LZ] and : Pinching theorem for the first eigenvalue on positively curved manifolds. Invent. Math., 65 (1981) 221-225. | Zbl | MR | EuDML
[MU] and : On the least positive eigenvalue of Laplacian for compact homogeneous spaces. Osaka J. Math., 17 (1980) 471-484. | Zbl | MR
[N 1] : On the minimum eigenvalues of the Laplacians in Riemannian manifolds, Sci. Papers Coll. Gen. Ed. Univ. Tokyo, 11 (1961) 177-182. | Zbl | MR
[N 2] : Stability of harmonic maps between symmetric spaces, Proc. Tulane, Lecture Note in Math. 949, Springer Verlag: New York (1982), 130-137. | Zbl | MR
[Sm] : The second variation formula for harmonic mappings. Proc. Amer. Math. Soc., 47 (1975) 229-236. | Zbl | MR
[Su] : Representation of compact groups realized by spherical functions on symmetric spaces. Proc. Japan Acad., 38 (1962) 111-113. | Zbl | MR
[T] : Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku Math. Jour. 36 (1984) 293-314. | Zbl | MR
[TK] : Minimal imbedding of R-spaces. J. Diff. Geom., 2 (1968) 203-215. | Zbl | MR
[U] : 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. | Zbl | MR
[W] : Compact homogeneous Riemannian manifolds with strictly positive curvature. Ann. Math., 96 (1972) 277-295. | Zbl | MR
[Wr] : Harmonic analysis on semi-simple Lie groups, I, Berlin, Heidelberg, New York: Springer Verlag (1972). | Zbl | MR






