Conformal transformation for prescribing scalar curvature on sphere
Main Article Content
Keywords
conformal metric, scalar curvature, Hilbert space, conformal transformation.
Abstract
In [1], Granados proved the existence of a whole family of conformal metrics to the Euclidean metric on Sn having scalar curvature n(n−1). In this paper, we find another solution to the problem of prescribing scalar curvature on Sn. Furthermore, if a family of solutions of the general problem is known, we get a new family of solutions.
MSC: 53.A30; 53.A10
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References
[1] C. Granados. Un caso particular del problema de prescribir la curvatura escalar en Sn. Matemáticas: Ense˜nanza Universitaria, pISSN 0120–6788, eISSN 1900-043X, XV(1), 119–123 (2007).
[2] T. Aubin. Some nonlinear problems in Riemannian Geometry, ISBN 3–540– 60752–8. Springer–Verlag, Berlin Heidelberg, 1998.
[3] R. Schoen. Conformal deformation of a Riemannian metric to constant scalar curvature. Journal of Differential Geometry, ISSN 0022–040X, 20(2), 479–495 (1984).
[4] R. Schoen and S. Yau. Lectures on Differential Geometry, Vol. 1, ISBN 1–57146– 012–8. International Press Publications, Boston, 1994. Referenciado en 48, 52
[5] W. Chen and C. Li. Prescribing scalar curvature on Sn. Pacific Journal of Mathematics, ISSN 0030–8730, 199(1), 61–78 (2001).
[6] C. Granados. Tesis de maestría: Sobre la existencia de una métrica conforme a la métrica euclidiana en la n−esfera. Universidad del Valle, Santiago de Cali, 2005.
[7] L. C. Evans. Partial differential equations, vol 19, ISBN 0–8218–0772–2.American Mathematical Society Providence, Rhode Island, 1998.
[8] W. Chen and W. Ding. Scalar curvatures on S2. Transactions of the American Mathematical Society, eISSN 1088–6850, pISSN 0002–9947, 303(1), 365–382 (1987).
[9] R. Schoen and D. Zhang. Prescribed scalar curvature on the n−sphere. Calculus of variations and partial differential equations, ISSN 0944–2669, 4(1), 1–25 (1996).
[2] T. Aubin. Some nonlinear problems in Riemannian Geometry, ISBN 3–540– 60752–8. Springer–Verlag, Berlin Heidelberg, 1998.
[3] R. Schoen. Conformal deformation of a Riemannian metric to constant scalar curvature. Journal of Differential Geometry, ISSN 0022–040X, 20(2), 479–495 (1984).
[4] R. Schoen and S. Yau. Lectures on Differential Geometry, Vol. 1, ISBN 1–57146– 012–8. International Press Publications, Boston, 1994. Referenciado en 48, 52
[5] W. Chen and C. Li. Prescribing scalar curvature on Sn. Pacific Journal of Mathematics, ISSN 0030–8730, 199(1), 61–78 (2001).
[6] C. Granados. Tesis de maestría: Sobre la existencia de una métrica conforme a la métrica euclidiana en la n−esfera. Universidad del Valle, Santiago de Cali, 2005.
[7] L. C. Evans. Partial differential equations, vol 19, ISBN 0–8218–0772–2.American Mathematical Society Providence, Rhode Island, 1998.
[8] W. Chen and W. Ding. Scalar curvatures on S2. Transactions of the American Mathematical Society, eISSN 1088–6850, pISSN 0002–9947, 303(1), 365–382 (1987).
[9] R. Schoen and D. Zhang. Prescribed scalar curvature on the n−sphere. Calculus of variations and partial differential equations, ISSN 0944–2669, 4(1), 1–25 (1996).