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Gradient Ricci solitons with semi-symmetry

박지연|조종택
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회보 (Bulletin of the KMS)|제51권 제1호|pp. 213-219

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키워드

gradient Ricci solitonssemi-symmetric spacesGaussian soliton
주제분류수학

초록

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form S3, H3, R3 (Gaussian soliton); or a product space R×S2, R×H2, where the potential function depends only on the nullity.

Abstract

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form S3, H3, R3 (Gaussian soliton); or a product space R×S2, R×H2, where the potential function depends only on the nullity.

참고문헌 (10)

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  4. R. S. Hamilton, "The Ricci flow on surfaces, Mathematics and general relativity (santa Cruz, CA, 1986)", pp.237~262 (1988), American Math. Soc
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  6. "The entropy formula for the Ricci flow and its geometric applications"[URL]
  7. P. Petersen, "Rigidity of gradient Ricci solitons", Pacific J. Math, 241(2), pp.329~345 (2009)
  8. K. Sekigawa, "On some 3-dimensional complete Riemannian manifolds satisfying R(X, Y ) · R = 0", Tˆohoku Math. J, 27(4), pp.561~568 (1975)
  9. Z. I. Szab´o, "Structure theorems on Riemannian spaces satisfying R(X, Y ) · R = 0. I. The Local version", J. Diff. Geom, 17(4), pp.531~582 (1982)
  10. Z. I. Szab´o, "Structure theorems on Riemannian spaces satisfying R(X, Y )·R = 0. II", Global versions, Geom. Dedicata, 19(1), pp.65~108 (1985)

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