Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 149, Issue 8, Pages 3575-3581Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15466
Keywords
Splitting theorem; weighted Laplacian; Laplacian comparison
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Funding
- National Natural Science Foundation of China [11701516]
- Scientific Research Foundation of Zhejiang Sci-Tech University [17062066-Y]
- Fundamental Research Funds of Zhejiang Sci-Tech University [2020Q043]
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For a gradient Ricci soliton (M, g, f) with certain conditions on a geodesic line gamma, the manifold will split off a line isometrically.
Let (M, g, f) be a gradient Ricci soliton del(2)f + Ric =lambda g with lambda is an element of {1/2, 0,- 1/2}. Suppose there is a geodesic line gamma : (-infinity,infinity) -> M satisfying lim inf t ->infinity integral(t)(0) Ric (gamma(s), gamma(s))ds +lim inf t ->-infinity integral(0)(t) Ric (gamma(s),gamma(s))ds >= 0, then (M, g, f) splits off a line isometrically.
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