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Abstract:

We establish the relationship between the scalar curvature of a warped product M xf N of Riemann manifolds and those ones of M and N. Then we search for weights f to obtain constant scalar curvature on M xf N when M is compact. © 1987 American Mathematical Society.

Registro:

Documento: Artículo
Título:Scalar curvature and warped products of riemann manifolds
Autor:Dobarro, F.; Lami Dozo, E.
Filiación:Departamento de Matemâtica, Universidad de Buenos Aires, Buenos Aires, Argentina
Instituto Argentino De Matematica, Conicet, Vlamonte 1636, Buenos Aires, 1055, Argentina
Palabras clave:Bifurcation from infinity; Nonlinear eigenvalue problem; Principal eigenvalue and eigenfunction
Año:1987
Volumen:303
Número:1
Página de inicio:161
Página de fin:168
DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0896013-4
Título revista:Transactions of the American Mathematical Society
Título revista abreviado:Trans. Am. Math. Soc.
ISSN:00029947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v303_n1_p161_Dobarro

Referencias:

  • Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces (1976) SIAM Rev, 18, pp. 620-709
  • Aubin, T., Nonlinear analysis on manifolds. Monge-Ampère equations A Series of Comprehensive Studies in Mathematics, 252. , Springer, Berlin
  • Aubin, T., Métriques Riemanniennes et courbure (1970) J. Differential Geom, 4, pp. 383-424
  • Berestycki, P., Le nombre de solutions de certains problèmes semi-linéaires elliptiques (1981) J. Funct. Anal, 40, pp. 1-29
  • Berger, M., Gauduchon, P., Mazet, E., Le spectre d'une variété Riemannienne (1971) Lecture Notes in Math, 194. , Springer
  • Bishop, R.L., O’Neill, B., Manifolds of negative curvature (1969) Trans. Amer. Math. Soc, 145, pp. 1-49
  • Clément, P.H., Peletier, L.A., An anti-maximum principle for second-order elliptic operators (1979) J. Differential Equations, 34, pp. 218-229
  • Crandall, M.G., Rabinowitz, P.H., Tartar, L., On a Dirichlet problem with a singular nonlinearity (1680) MRC Report, p. 1976
  • Ejiri, N., A negative answer to a conjecture of conformal transformations of Riemann manifolds (1981) J. Math. Soc. Japan, 33, pp. 261-266
  • Ejiri, N., Some compact hypersurfaces of constant scalar curvature in a sphere (1982) J. Geom, 19, pp. 197-199
  • Lions, P.L., On the existence of positive solutions of semilinear elliptic equations (1982) SIAM Rev, 24, pp. 441-467
  • Moser, J., On a nonlinear problem in differential geometry (1973) Dynamical Systems, M. M. Peixoto, pp. 273-280. , (ed), Academic Press, New York
  • Rabinowitz, P.H., Some global results for nonlinear eigenvalue problems (1971) J. Funct. Anal, 7, pp. 487-513
  • Rabinowitz, P.H., On bifurcation from infinity (1973) J. Differential Equations, 14, pp. 462-475
  • Turner, E.E.L., Positive solutions of nonlinear eigenvalue problems (1974) C.I.M.E. Varenna, pp. 212-239
  • Yamabe, H., On a deformation of Riemannian structures on compact manifolds (1960) Osaka Math. J, 12, pp. 21-37
  • Zucker, S., L2 cohomology of warped products and arithmetic groups (1982) Invent. Math, 70, pp. 169-218

Citas:

---------- APA ----------
Dobarro, F. & Lami Dozo, E. (1987) . Scalar curvature and warped products of riemann manifolds. Transactions of the American Mathematical Society, 303(1), 161-168.
http://dx.doi.org/10.1090/S0002-9947-1987-0896013-4
---------- CHICAGO ----------
Dobarro, F., Lami Dozo, E. "Scalar curvature and warped products of riemann manifolds" . Transactions of the American Mathematical Society 303, no. 1 (1987) : 161-168.
http://dx.doi.org/10.1090/S0002-9947-1987-0896013-4
---------- MLA ----------
Dobarro, F., Lami Dozo, E. "Scalar curvature and warped products of riemann manifolds" . Transactions of the American Mathematical Society, vol. 303, no. 1, 1987, pp. 161-168.
http://dx.doi.org/10.1090/S0002-9947-1987-0896013-4
---------- VANCOUVER ----------
Dobarro, F., Lami Dozo, E. Scalar curvature and warped products of riemann manifolds. Trans. Am. Math. Soc. 1987;303(1):161-168.
http://dx.doi.org/10.1090/S0002-9947-1987-0896013-4