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A 3-DIMENSIONAL SASAKIAN METRIC AS A YAMABE SOLITON

RAMESH SHARMA

Department of Mathematics, University of New Haven, West Haven, CT 06516, USA

https://doi.org/10.1142/S0219887812200034Cited by:31 (Source: Crossref)

Abstract

If a 3-dimensional Sasakian metric on a complete manifold (M, g) is a Yamabe soliton, then we show that g has constant scalar curvature, and the flow vector field V is Killing. We further show that, either M has constant curvature 1, or V is an infinitesimal automorphism of the contact metric structure on M.

Keywords:

AMSC: 53C25, 53C21, 53C44

References

D. E. Blair , Riemannian Geometry of Contact and Symplectic Manifolds ( Birkhäuser , Boston , 2010 ) . Crossref, Google Scholar
D. E. Blair, T. Koufogiorgos and R. Sharma, Kodai Math. J. 13, 391 (1990). Crossref, Web of Science, Google Scholar
B. Chow , P. Lu and L. Ni , Hamilton's Ricci Flow , Graduate Studies in Mathematics 77 ( American Mathematical Society , Science Press , 2006 ) . Crossref, Google Scholar
R. S. Hamilton, Lectures on geometric flows, unpublished manuscript (1989) . Google Scholar
R. Sharma and D. E. Blair, Illinois J. Math. 40, 553 (1996). Crossref, Web of Science, Google Scholar
R. Sharma and A. Ghosh, Int. J. Geom. Meth. Mod. Phys. 8, 149 (2011). Link, Web of Science, Google Scholar
S. Tanno, Tohoku Math. J. 14, 416 (1962). Crossref, Google Scholar
S. Tanno, Tohoku Math. J. 15, 140 (1963). Crossref, Google Scholar
K. Yano , Integral Formulas in Riemannian Geometry ( Marcel Dekker , New York , 1970 ) . Google Scholar