The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold

Hajime Urakawa

Compositio Mathematica (1986)

  • Volume: 59, Issue: 1, page 57-71
  • ISSN: 0010-437X

How to cite

top

Urakawa, Hajime. "The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold." Compositio Mathematica 59.1 (1986): 57-71. <http://eudml.org/doc/89782>.

@article{Urakawa1986,
author = {Urakawa, Hajime},
journal = {Compositio Mathematica},
keywords = {symmetric spaces; homogeneous space; first eigenvalue; Laplacian; harmonic map},
language = {eng},
number = {1},
pages = {57-71},
publisher = {Martinus Nijhoff Publishers},
title = {The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold},
url = {http://eudml.org/doc/89782},
volume = {59},
year = {1986},
}

TY - JOUR
AU - Urakawa, Hajime
TI - The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 59
IS - 1
SP - 57
EP - 71
LA - eng
KW - symmetric spaces; homogeneous space; first eigenvalue; Laplacian; harmonic map
UR - http://eudml.org/doc/89782
ER -

References

top
  1. [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. Zbl0362.53033MR370624
  2. [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. MR699924
  3. [BBG] P. Berard, G. Besson and S. Gallot: Sur une inegalite isoperimetrique qui generalise celle de Paul Levy-Gromov. Invent. Math., (1985). Zbl0571.53027
  4. [BB 1] L. Btrard Bergery: Sur certaines fibrations d'espaces homogenes riemanniens. Compos. Math., 30 (1975), 43-61. Zbl0304.53036MR370432
  5. [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. Zbl0289.53037MR417987
  6. [BBB] L. Bérard Bergery and J.P. Bourguignon: Laplacians and Riemannian submersions with totally geodesic fibers. Illinois J. Math., 26 (1982) 181-200. Zbl0483.58021MR650387
  7. [B] M. Berger: Les variétés riemanniennes homogenes normales simplement connexes a courbure strictement positive. Ann. Scuol. Norm. Sup. Pisa, 15 (1961) 179-246. Zbl0101.14201MR133083
  8. [Bo] N. Bourbaki: Groupes et algèbres de Lie, Chap. 4, 5 et 6, Paris: Herman (1968). Zbl0483.22001MR240238
  9. [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. Zbl0327.43013MR397801
  10. [C] C.B. Croke: An eigenvalue pinching problem. Invent. Math., 68 (1982) 253-256. Zbl0505.53018MR666162
  11. [H] H.M. Huang: Some remarks on the pinching problems. Bull. Inst. Math. Acad. Sinica, 9 (1981) 321-340. Zbl0477.53043MR625725
  12. [He] S. Helgason: Differential geometry and symmetric spaces, New York: Academic Press (1962). Zbl0111.18101MR145455
  13. [KN] S. Kobayashi and K. Nomizu: Foundations of differential geometry, II, New York: Interscience (1969). Zbl0175.48504
  14. [LT] P. Li and A.E. Treibergs: Pinching theorem for the first eigenvalue on positively curved four-manifolds. Invent. Math., 66 (1982) 35-38. Zbl0496.53032MR652644
  15. [LZ] P. Li and J.Q. Zhong: Pinching theorem for the first eigenvalue on positively curved manifolds. Invent. Math., 65 (1981) 221-225. Zbl0496.53031MR641128
  16. [MU] H. Muto and H. Urakawa: On the least positive eigenvalue of Laplacian for compact homogeneous spaces. Osaka J. Math., 17 (1980) 471-484. Zbl0446.53037MR587767
  17. [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. Zbl0134.31005MR144283
  18. [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. Zbl0507.58019MR673587
  19. [Sm] R.T. Smith: The second variation formula for harmonic mappings. Proc. Amer. Math. Soc., 47 (1975) 229-236. Zbl0303.58008MR375386
  20. [Su] M. Sugiura: Representation of compact groups realized by spherical functions on symmetric spaces. Proc. Japan Acad., 38 (1962) 111-113. Zbl0134.26901MR142689
  21. [T] M. Takeuchi: Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku Math. Jour.36 (1984) 293-314. Zbl0528.53047MR742600
  22. [TK] M. Takeuchi And S. Kobayashi: Minimal imbedding of R-spaces. J. Diff. Geom., 2 (1968) 203-215. Zbl0165.24901MR239007
  23. [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. Zbl0548.53045MR755857
  24. [W] N.R. Wallach: Compact homogeneous Riemannian manifolds with strictly positive curvature. Ann. Math., 96 (1972) 277-295. Zbl0261.53033MR307122
  25. [Wr] G. Warner: Harmonic analysis on semi-simple Lie groups, I, Berlin, Heidelberg, New York: Springer Verlag (1972). Zbl0265.22020MR498999

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.