Abstract
Studying self-similar solutions of geometric flows on manifolds plays an important role in understanding geometrical and topological properties of underlying manifolds. In this paper, we prove that a complete shrinking Ricci–Bourguignon harmonic flow soliton [Formula: see text] is compact if and only if [Formula: see text] is bounded on [Formula: see text]. Also, we show that a complete shrinking Ricci–Bourguignon harmonic flow soliton has finite fundamental group.
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