[1] Besse A L. Einstein Manifolds. New York:Springer Verlag, 1987
[2] Nagano T, Yano K. Einstein spaces admitting a one-parameter group of conformal transformations. Ann of Math, 1959, 69:451-461
[3] Yano K, Obata M. Conformal changes of Riemannian metrics. J Diff Geom, 1970, 4:53-72
[4] Deshmukh S, Al-Solamy F R. Conformal gradient vector fields on a compact Riemannian manifold. Colloquium Math, 2008, 112(1):157-161
[5] Goldberg S I. Manifolds admitting a one-parameter group of conformal transformations. Michigan Math J, 1968, 15:339-344
[6] Nagano T. The conformal transformation on a space with parallel Ricci tensor. Journal of the Mathematical Society of Japan, 1959, 11(1):10-14
[7] Obata M. Quelques inegalites integrates sur une variete riemannienne compacte. C R Acad Sci Paris, 1967, 264:123-125
[8] Yano K, Nagano T. Einstein spaces admitting a one-parameter group of conformal transformations. Ann of Math, 1959, 69(2):451-461
[9] Yano K. On Riemannian manifolds with constant scalar curvature admitting a conformal transformation group. Proc Nat Acad Sci USA, 1966, 55:472-476
[10] Alodan H. Conformal gradient vector fields. Differ Geom Dyn Syst, 2010, 12:1-3
[11] Ejiri N. A negative answer to a conjecture of conformal transformations of Riemannian manifolds. J Math Soc Japan, 1981, 33:261-266
[12] Yano K. Integral Formulas in Riemannian Geometry. New York:Marcel Dekker, 1970
[13] Deshmukh S, Al-Solamy F R. Conformal vector fields and conformal transformations on a Riemannian manifold. Balkan J Geom Appl, 2012, 17(1):9-16
[14] Ackler L L, Hsiung C C. Isometry of Riemannian manifolds to spheres. Annali di Matematica Pura ed Applicata, 1974, 99(1):53-64
[15] Hsiung C C, Mugridge L R. Conformal changes of metrics on a Riemannian manifold. Math Z, 1971, 119:179-187
[16] Limoncu M. The Bochner technique and modification of the Ricci tensor. Annals of Global Analysis and Geometry, 2009, 36(3):285-291
[17] Lichnerowicz A. Geometrie des Groupes de Transformations. Paris:Dunod, 1958
[18] Obata M. Certein conditions for a Riemannian manifods to be isometric with a sphere. J Math Soc Japan, 1962, 14:333-340
[19] Ruan Q H, Chen F. Eigenvalue problems on Riemannian manifolds with a modified Ricci tensor. Annals of Global Analysis and Geometry, 2014, 46:63-74 |