Short CommunicationsNo Access

ALMOST CONTACT 3-MANIFOLDS AND RICCI SOLITONS

JONG TAEK CHO

Department of Mathematics, Chonnam National University, Gwangju 500-757, Korea

https://doi.org/10.1142/S0219887812200228Cited by:20 (Source: Crossref)

Abstract

A Kenmotsu 3-manifold M admitting a Ricci soliton (g, w) with a transversal potential vector field w (orthogonal to the Reeb vector field) is of constant sectional curvature -1. A cosymplectic 3-manifold admitting a Ricci soliton with the Reeb potential vector field or a transversal vector field is of constant sectional curvature 0.

Keywords:

AMSC: 53C15, 53C25, 53C44

References

D. E. Blair , Riemannian Geometry of Contact and Symplectic Manifolds , Progress in Mathematics 203 ( Birkhäuser , Boston , 2002 ) . Crossref, Google Scholar
H.-D. Cao, Chinese Ann. Math. Ser. B 27, 121 (2006), DOI: 10.1007/s11401-005-0379-2. Crossref, Web of Science, Google Scholar
J. T. Cho, Proc. Edinb. Math. Soc. 54, 47 (2011), DOI: 10.1017/S0013091509000571. Crossref, Web of Science, Google Scholar
B. Chow and D. Knopf , The Ricci Flow: An Introduction , Mathematical Surveys and Monographs 110 ( American Mathematical Society , 2004 ) . Crossref, Google Scholar
D. Chinea, M. de Leon and J. C. Marrero, J. Math. Pures Appl. 72, 567 (1993). Web of Science, Google Scholar
D. Friedan, Ann. Physics 163, 318 (1985), DOI: 10.1016/0003-4916(85)90384-7. Crossref, Web of Science, Google Scholar
S. I. Goldberg and K. Yano, Pacific J. Math. 31, 373 (1969). Crossref, Web of Science, Google Scholar
R. S. Hamilton, J. Differential Geom. 17, 255 (1982). Crossref, Web of Science, Google Scholar
J. Isenberg and M. Jackson, J. Differential Geom. 35, 723 (1992). Crossref, Web of Science, Google Scholar
K. Kenmotsu, Tôhoku Math. J. 24, 93 (1972), DOI: 10.2748/tmj/1178241594. Crossref, Web of Science, Google Scholar
S. Tanno, Tôhoku Math. J. 21, 21 (1969), DOI: 10.2748/tmj/1178243031. Crossref, Web of Science, Google Scholar