Conformal indices of riemannian manifolds

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1. [1] M. Berger, P. Gauduchon, and E. Mazet: Le Spectre d'une Variété Riemannienne. Springer-Verlag, Berlin (1971). Zbl0223.53034MR282313
2. [2] D. Bleecker: Determination of a Riemannian metric from the first variation of its spectrum. Amer. J. Math.107 (1985) 815-831. Zbl0577.58032MR796904
3. [3] T. Branson: Conformally covariant equations on differential forms. Comm. in P.D.E.7 (1982) 392-431. Zbl0532.53021MR652815
4. [4] T. Branson: Differential operators canonically associated to a conformal structure. Math. Scand.57 (1985) 293-345. Zbl0596.53009MR832360
5. [5] T. Branson and B. Ørsted: Conformal spectral geometry, preprint. Purdue University (1984). 
6. [6] D. Burns, K. Diederich and S. Shnider: Distinguished curves in pseudoconvex boundaries. Duke Math. J.44 (1977) 407-431. Zbl0382.32011MR445009
7. [7] I. Chavel: Eigenvalues in Riemannian Geometry. Academic Press, New York (1984). Zbl0551.53001MR768584
8. [8] Y. Choquet-Bruhat and D. Christodoulou: Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in 3 + 1 dimensions. A nn. Sci. École Norm. Sup. (4) 14 (1981) 481-500. Zbl0499.35076MR654209
9. [9] J. Dowker and G. Kennedy: Finite temperature and boundary effects in static space-times. J. Phys.A11 (1978) 895-920. MR479266
10. [10] C. Fefferman: Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains. Ann. of Math.103 (1976) 395-416. Zbl0322.32012MR407320
11. [11] C. Fefferman and C.R. Graham: Conformal invariants. Proceedings of the Symposium: Elie Cartan et les mathématiques d'aujourd'hui, Asterisque, to appear. Zbl0602.53007MR837196
12. [12] F. Friedlander: The Wave Equation on a Curved Space-time. Cambridge University Press (1975). Zbl0316.53021MR460898
13. [13] P. Gilkey: The Index Theorem and the Heat Equation. Publish or Perish, Boston (1974). Zbl0287.58006MR458504
14. [14] P. Gilkey: Spectral geometry of a Riemannian manifold. J. Diff. Geom.10 (1975) 601-618. Zbl0316.53035MR400315
15. [15] P. Gilkey: Lefschetz fixed point formulas and the heat equation, in Partial Differential Equations and Geometry, C. Byrnes (ed.), Lecture Notes in Pure and Applied Mathematics, Vol.. 48. Marcel Dekker Inc., New York (1979). Zbl0405.58044MR535591
16. [16] P. Gilkey: The spectral geometry of the higher order Laplacian. Duke Math. J.47 (1980) 511-528. Zbl0448.58026MR587163
17. [17] P. Gilkey: Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem. Publish or Perish, Wilmington, Delaware (1984). Zbl0565.58035MR783634
18. [18] P. Günther and V. Wünsch: On some polynomial conformal tensors. Math. Nachr.124 (1985), 217-238. Zbl0592.53012MR827899
19. [19] S. Hawking: Zeta function regularization of path integrals in curved spacetime. Commun. Math. Phys.55 (1977) 133-148. Zbl0407.58024MR524257
20. [20] S. Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York (1978). Zbl0451.53038MR514561
21. [21] D. Jerison and J.M. Lee: A subelliptic, nonlinear eigenvalue problem and scalar curvature on CR manifolds. in Microlocal Analysis. Contemporary Math. 27 (1984) 57-63. Zbl0577.53035MR741039
22. [22] Y. Kosmann: Dérivées de Lie des spineurs. Ann. Mat. Pura Appl. (4) XCI (1972) 317-395. Zbl0231.53065MR312413
23. [23] Y. Kosmann: Degrés conformes des laplaciens et des opérateurs de Dirac. C.R. Acud. Soi. Paris Ser. A280 (1975) 283-285. Zbl0296.53012MR391187
24. [24] R. Kubawara: On isospectral deformations of Riemannian metrics II. Compositio Math.47 (1982) 195-205. Zbl0505.53019MR677020
25. [25] J. Lee: The Fefferman metric and pseudohermitian invariants, preprint. Harvard University (1985). 
26. [26] K. Miller and F. Murray: Existence Theorems for Ordinary Differential Equations. New York University Press (1954). Zbl0056.31301MR64934
27. [27] S. Paneitz: A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds, preprint. M.I.T. (1983). 
28. [28] T. Parker and S. Rosenberg: Invariants of conformal Laplacians, preprint. Brandeis University (1985). 
29. [29] D. Ray and I. Singer: R-torsion and the Laplacian on Riemannian manifolds. Advances in Math.7 (1971) 145-210. Zbl0239.58014MR295381
30. [30] S. Rosenberg: The variation of the Rham zeta function, preprint. Brandeis University (1984). MR869220
31. [31] R. Schimming: Lineare Differentialoperatoren zweiter Ordnung mit metrischem Hauptteil und die Methode der Koinzidenzwerte in der Riemannschen Geometrie. Beitr. z. Analysis15 (1981) 77-91. Zbl0504.35021MR614779
32. [32] R. Seeley: Complex powers of an elliptic operator. Proc. Symp. Pure and Applied Math.10 (1967) 288-307. Zbl0159.15504MR237943
33. [33] P. Seeley: Topics in pseudo-differential operators, in Pseudo-Differential Operators. Centro Internazionale Mathematico Estivo (1969). 
34. [34] V. Wünsch: Konforminvariante Variationsprobleme und Huygenssches Prinzip. Math. Nachr.120 (1985) 175-193. MR808340

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