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  JP Journal of Geometry and Topology  
 ISSN: 0972-415X
 
 
 

     JP Journal of Geometry and Topology
    Volume 8, Issue 1, Pages 93 - 102 (March 2008)


SPECTRUM OF AN EINSTEIN-LIKE MANIFOLD

Sharief Deshmukh (Saudi Arabia)

Received March 31, 2008; Revised April 20, 2008

References:



[1] L. A. Besse, Einstein Manifolds, Springer-Verlag, 1987.

[2] S. Bochner, Vector fields and Ricci curvature, AMS Bull. 52 (1946), 776-797.

[3] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.

[4] S. Deshmukh and A. Al-Eid, Curvature bounds for the spectrum of a compact Riemannian manifold of constant scalar curvature, J. Geom. Anal. 15(4) (2005), 589-606.

[5] A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedi. 7 (1968), 259-280.

[6] P. Li, Lecture Notes on Geometric Analysis, Res. Inst. Math. Global Analysis Research Center SNU, No. 6 (1993).

[7] P. Li and S. T. Yau, Eigenvalues of a compact Riemannian manifold, AMS Proc. Symp. Pure Math. 36 (1980), 205-239.

[8] M. Obata, Certain conditions for a Riemannian manifold to be isometric to the sphere, J. Math. Soc. Japan 14 (1962), 333-340.

[9] U. Simon, Curvature bounds for the spectrum of a closed Einstein spaces, Can. J. Math. XXX(4) (1978), 1087-1091.

[10] S. T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Scient. Ec. Norm. Sup. 4 (1985), 487-507.

[11] S. T. Yau, Problem Section, Seminar on Differential Geometry, Princeton Univ. Press, 1982.

[12] J. Q. Zong and H. C. Wang, On the estimate of first eigenvalue of a compact Riemannian manifold, Sci. Sinica Ser. A 27 (1984), 1265-1273.

Keywords and phrases: Ricci curvature, eigenvalues, eigenfunctions, Laplacian operator.

Communicated by Yasuo Matsushita

 


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