TY - JOUR
T1 - A gap theorem on complete shrinking gradient Ricci solitons
AU - Zhang, Shijin
N1 - Publisher Copyright:
© 2017 American Mathematical Society.
PY - 2018
Y1 - 2018
N2 - In this short note, using Günther’s volume comparison theorem and Yokota’s gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton (Mn, g, f) with sectional curvature K(g) < A and Volf (M) ≥ v for some uniform constant A, v, there exists a small uniform constant ɛn,A,v > 0 depends only on n, A and v, if the scalar curvature R ≤ ɛn,A,v, then (M, g, f) is isometric to the Gaussian soliton (Formula Presented).
AB - In this short note, using Günther’s volume comparison theorem and Yokota’s gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton (Mn, g, f) with sectional curvature K(g) < A and Volf (M) ≥ v for some uniform constant A, v, there exists a small uniform constant ɛn,A,v > 0 depends only on n, A and v, if the scalar curvature R ≤ ɛn,A,v, then (M, g, f) is isometric to the Gaussian soliton (Formula Presented).
KW - Gap theorem
KW - Sectional curvature
KW - Shrinking gradient Ricci solitons
UR - https://www.scopus.com/pages/publications/85034232720
U2 - 10.1090/proc/13689
DO - 10.1090/proc/13689
M3 - 文章
AN - SCOPUS:85034232720
SN - 0002-9939
VL - 146
SP - 359
EP - 368
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -