DOI QR코드

DOI QR Code

ON THE SOLUTIONS OF THE (λ, n + m)-EINSTEIN EQUATION

Hwang, Seungsu

  • Received : 2013.11.06
  • Published : 2014.07.31

Abstract

In this paper, we study the structure of m-quasi Einstein manifolds when there exists another distinct solution to the (${\lambda}$, n + m)-Einstein equation. In particular, we derive sufficient conditions for the non-existence of such solutions.

Keywords

Bakry-Emery Ricci tensor;quasi-Einstein manifolds;the (${\lambda}$, n + m)-Einstein equation

References

  1. J. Case, Y. Shu, and G. Wei, Rigidity of quasi-Einstein metrics, Differential Geom. Appl. 29 (2011), no. 1, 93-100. https://doi.org/10.1016/j.difgeo.2010.11.003
  2. M. Fernandez-Lopez and E. Garcia-Rio, Rigidity of shrinking Ricci solitons, Math. Z. 269 (2011), no. 1-2, 461-466. https://doi.org/10.1007/s00209-010-0745-y
  3. C. He, P. Petersen, and W. Wylie, On the classification of warped product Einstein metrics, Comm. Anal. Geom. 20 (2012), no. 2, 271-311. https://doi.org/10.4310/CAG.2012.v20.n2.a3
  4. O. Munteanu and N. Sesum, On gradient Ricci solitons, J. Geom. Anal. 23 (2013), no. 2, 539-561. https://doi.org/10.1007/s12220-011-9252-6
  5. P. Petersen and W.Wylie, Rigidity of gradient Ricci solitons, Pacific J. Math. 241 (2009), no. 2, 329-345. https://doi.org/10.2140/pjm.2009.241.329
  6. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965), 251-275. https://doi.org/10.1090/S0002-9947-1965-0174022-6
  7. A. L. Besse, Einstein Manifolds, New York, Springer-Verlag, 1987.
  8. H. D. Cao and Q. Chen, On Bach-flat gradient shrinking Ricci solitons, Duke Math. J. 162 (2013), no. 6, 1149-1169. https://doi.org/10.1215/00127094-2147649

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)