Let π:P(O(0)⊕O(k))→Pn-1\documentclass[12pt]{minimal}
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\begin{document}$$\pi :{\mathbb {P}}({\mathcal {O}}(0)\oplus {\mathcal {O}}(k))\rightarrow {\mathbb {P}}^{n-1}$$\end{document} be a projective bundle over Pn-1\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {P}}^{n-1}$$\end{document} with 1≤k≤n-1\documentclass[12pt]{minimal}
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\begin{document}$$1\le k \le n-1$$\end{document}. We denote P(O(0)⊕O(k))\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {P}}({\mathcal {O}}(0)\oplus {\mathcal {O}}(k))$$\end{document} by Nkn\documentclass[12pt]{minimal}
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\begin{document}$$N_{k}^{n}$$\end{document} and endow it with the U(n)-invariant gradient shrinking Kähler Ricci soliton structure constructed by Cao (Elliptic and parabolic methods in geometry (Minneapolis, MN, 1994), A K Peters, Wellesley, 1996) and Koiso (Recent topics in differential and analytic geometry. Advanced studies in pure mathematics, Boston, 1990). In this paper, we show that lens space L(k;1)(r)\documentclass[12pt]{minimal}
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\begin{document}$$L(k\, ;1)(r)$$\end{document} with radius r embedded in Nkn\documentclass[12pt]{minimal}
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\begin{document}$$N_{k}^{n}$$\end{document} is a self-similar solution. We also prove that there exists a pair of critical radii r1<r2\documentclass[12pt]{minimal}
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\begin{document}$$r_{1}<r_{2}$$\end{document}, which satisfies the following. The lens space L(k;1)(r)\documentclass[12pt]{minimal}
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\begin{document}$$L(k\, ;1)(r)$$\end{document} is a self-shrinker if r<r2\documentclass[12pt]{minimal}
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\begin{document}$$r<r_{2}$$\end{document} and self-expander if r2<r\documentclass[12pt]{minimal}
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\begin{document}$$r_{2}<r$$\end{document}, and the Ricci-mean curvature flow emanating from L(k;1)(r)\documentclass[12pt]{minimal}
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\begin{document}$$L(k\, ;1)(r)$$\end{document} collapses to the 0-section of π\documentclass[12pt]{minimal}
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\begin{document}$$\pi $$\end{document} if r<r1\documentclass[12pt]{minimal}
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\begin{document}$$r<r_{1}$$\end{document} and to the ∞\documentclass[12pt]{minimal}
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\begin{document}$$\infty $$\end{document}-section of π\documentclass[12pt]{minimal}
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\begin{document}$$\pi $$\end{document} if r1<r\documentclass[12pt]{minimal}
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\begin{document}$$r_{1}<r$$\end{document}. This paper gives explicit examples of Ricci-mean curvature flows.
