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The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton $(M^n ,g, f, \lambda)$ with constant scalar curvature admitting a non-homothetic conformal vector field $V$ leaving the potential vector field invariant. We show that in such manifolds the potential function $f$ is constant and the scalar curvature of $g$ is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field $V$, without constant scalar curvature assumption, we show that $g$ has constant curvature and determines the potential function $f$ explicitly.
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참고문헌 (7)
참고문헌 신청
A. L. Besse / 1987 / Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10 / Springer-Verlag,
Huai-Dong Cao / 2012 / On the structure of gradient Yamabe solitons / Mathematical Research Letters 19(4):767~774
GIOVANNI CATINO / 2012 / ON THE GLOBAL STRUCTURE OF CONFORMAL GRADIENT SOLITONS WITH NONNEGATIVE RICCI TENSOR / Communications in Contemporary Mathematics 14(06):1250045
P. Daskalopoulos / 2013 / The classification of locally conformally flat Yamabe solitons / Adv. Math 240:346~369
R. Hamilton / 1989 / Lectures on geometric flows
Huai-Dong Cao / 2012 / On the structure of gradient Yamabe solitons / Mathematical Research Letters 19(4):767~774
GIOVANNI CATINO / 2012 / ON THE GLOBAL STRUCTURE OF CONFORMAL GRADIENT SOLITONS WITH NONNEGATIVE RICCI TENSOR / Communications in Contemporary Mathematics 14(06):1250045
P. Daskalopoulos / 2013 / The classification of locally conformally flat Yamabe solitons / Adv. Math 240:346~369
R. Hamilton / 1989 / Lectures on geometric flows
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