A VALEURS COMPLEXES serait alors intéressant d'avoir une expression pour la courbure de Ricci associéè a une submersion semi-conforme (M 4 , g) ? (N 2 , h). classe d'applications semi-conformes de (M 4 , g) ? (N 2 , h) : les applications semi-conformes ? : (M 4 , g) ? (N 2 , h) qui se factorisent comme ? = ? ?? o` u ? : (M 4 , g) ? (P 3 , k) est un morphisme harmonique et ? : (P 3 , k) ? (N 2 , h) est semi'idées, P. Baird, A. Fardoun et S. Ouakkas ont montré que cela est vrai, mais la conditionétantconditionétant tellement compliquée, ils n'ont pas pu en déduire des conséquences harmonique généralisé, il nous semble toutàtoutà fait abordable, de chercherà chercherà caractériser ces morphismes d ,
,
,
Polynômes semi-conformes et morphismes harmoniques, Math.Z, vol.231, pp.589-604, 1999. ,
Harmonic morphisms onto Riemann surfaces and generalized analytic functions, Ann. Inst. Fourier (Grenoble), vol.37, issue.1, pp.135-173, 1987. ,
Explicit constructions of Ricci solitons, Variational Problems in Differential Geometry, vol.394, pp.37-55, 2012. ,
Conformal subfoliations of prescribed geodesic curvature, Mathematica Scandinavica, vol.93, pp.221-239, 2003. ,
Three-dimensional Ricci solitons which project to surfaces, vol.608, pp.65-91, 2007. ,
, CR geometry and conformal foliations, vol.44, pp.73-90, 2013.
On functions with a conjugate, Ann. Inst. Fourier (Gernoble), vol.65, issue.1, pp.277-314, 2015. ,
A conservation law for harmonic maps, Geometry Symp, vol.894, p.125, 1980. ,
Conformal and semi-conformal biharmonic maps, Ann. Glob. Anal. Geom, vol.34, pp.403-414, 2008. ,
Harmonic morphisms on heaven spaces, Bull. London Math. Soc, vol.41, issue.2, pp.198-204, 2009. ,
Bernstein Theorems for harmonic morphisms from R 3 and S 3, Math. Ann, vol.280, pp.579-603, 1988. ,
Harmonic morphisms between Riemannian manifolds, New Series, vol.29, 2003. ,
Brownian motion and generalized analytic and inner functions, Ann. Inst. Fourier (Grenoble), vol.29, issue.1, pp.207-228, 1979. ,
, Immortal homogeneous Ricci flows, 2017.
Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere, Annals of Mathematics, vol.177, issue.1, pp.1-52, 2013. ,
, Lectures on potential theory, 1967.
Harmonic morphisms with fibres of dimension one, Comm. Anal. Geom, vol.8, pp.219-265, 2000. ,
The Ricci flow : an introduction, Mathematical Surveys and Monographs, vol.110, 2004. ,
DOI : 10.1090/surv/110
, The Ricci Flow : Techniques and Applications, vol.135, 2007.
, The Ricci Flow : Techniques and Applications, vol.144, 2008.
DOI : 10.1090/surv/163
Compactifications of harmonic spaces, Nagoya Math. J, vol.25, pp.1-57, 1965. ,
DOI : 10.1017/s0027763000011454
URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/367B49D8130787844F83EA49BF5221F1/S0027763000011454a.pdf/div-class-title-compactifications-of-harmonic-spaces-div.pdf
, Structures Conformes, 2004.
Construction de métriques d'EinsteinàEinsteinà partir de transformations biconformes, Ann. Fac. des Sciences de Toulouse, Sér, vol.6, issue.3, pp.553-588, 2006. ,
DOI : 10.5802/afst.1129
URL : http://afst.cedram.org/cedram-bin/article/AFST_2006_6_15_3_553_0.pdf
Foundation of Modern Analysis, 1969. ,
Harmonic mappings of Riemannian manifolds, American Journal of Mathematics, vol.86, pp.109-160, 1964. ,
Methods inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti, chapter Additamentum 1. eulerarchive. org E065, p.1744 ,
, , 2018.
Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble), vol.28, issue.2, pp.107-144, 1978. ,
DOI : 10.5802/aif.691
URL : https://aif.centre-mersenne.org/article/AIF_1978__28_2_107_0.pdf
Multivalued harmonic morphisms, Math. Scand, vol.73, pp.127-155, 1993. ,
Linear stability of homogeneous Ricci solitons, Int. Math. Res. Not, vol.30, p.pp, 2006. ,
Three-manifolds with positive Ricci curvature, J. Differential Geom, vol.17, issue.2, pp.255-306, 1982. ,
DOI : 10.4310/jdg/1214436922
URL : https://doi.org/10.4310/jdg/1214436922
The analysis of linear partial differential operators, vol.1, 1983. ,
A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ, vol.19, pp.215-229, 1979. ,
Ueber eine particulre Lsung der partiellen Differentialgleichung ? 2 V ?x 2 + ? 2 V ?y 2 + ? 2 V ?z 2 = 0. Cr, vol.36, pp.113-134, 1848. ,
Local existence of Ricci solitons, Manuscripta Math, vol.91, pp.151-162, 1996. ,
DOI : 10.1007/bf02567946
Scalar curvature and conformal deformation of Riemannian structure, J. Differential Geom, vol.10, pp.113-134, 1975. ,
Zur Theorie der partiellen Differentialgleichung, Journal für die reine und angewandte Mathematik, vol.80, p.132, 1875. ,
Leçons sur la théorie analytique de la chaleur, 1861. ,
, The characterization of biharmonic morphisms, Differential geometry and its applications, vol.3, pp.31-41, 2001.
Biharmonic maps and morphisms from conformal mappings, Tohoku Math J, vol.62, issue.1, pp.55-73, 2010. ,
On the long-time behavior of type-III Ricci flow solutions, Math. Annalen, vol.339, pp.627-666, 2007. ,
Biharmonic classification of Riemannian manifolds, Bull. Amer. Math. Soc, vol.77, pp.432-436, 1971. ,
Construction of conjugate functions, Ann. Global Anal. Geom, vol.37, pp.321-326, 2010. ,
On constructions of harmonic morphisms into Euclidean spaces, J. Guangxi University for Nationalities, vol.2, pp.1-6, 1996. ,
, Biharmonic morphisms between Riemannian manifolds, Geometry and topology of submanifolds, X (Beijing, pp.231-239, 1999.
Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces, Jour. Geom. Phys, vol.62, pp.751-762, 2012. ,
Biharmonic Riemannian submersions from 3-manifolds, Math Zeitschrift, vol.269, issue.3, pp.917-925, 2011. ,
A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (summary), SIGMA. Symmetry, Integrability and Geometry. Methods and Applications, vol.4, 2008. ,
, The entropy formula for the Ricci flow and its geometric applications
, Ricci flow with surgery on three-manifolds
, Finite extinction time for solutions to the Ricci flow on certain threemanifolds
The geometries of 3-manifolds, Bull. London Math. Soc, vol.15, pp.401-487, 1983. ,
, , vol.IV, pp.455-500, 1979.
, Three-dimensional Geometry and Topology, vol.1, 1997.
Harmonic morphisms from Einstein 4-manifolds to Riemann surfaces, Internat. J. Math, vol.14, issue.3, pp.327-337, 2003. ,
, Aspects twistoriels des applications semi-conformes, Thesis. Mathématiques, 2009.
Inversive Geometry, 1981. ,
Harmonic morphisms and Hermitian structures on Einstein 4manifolds, Internat. J. Math, vol.3, pp.415-439, 1992. ,