In this note we show that, under certain curvature positivity conditions (the weak PIC - 2 condition or the nonnegative bisectional curvature condition), a complete and noncompact expanding breather of the Ricci flow is also an expanding gradient Ricci soliton. This is the first no expanding breather theorem in the noncompact category.
Bibliographical noteFunding Information:
Liang Cheng’s Research partially supported by Natural Science Foundation of Hubei 2019CFB511.
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
- Expanding breathers
- Gradient expanding Ricci solitons
- No breather theorem
- Noncompact Ricci flows