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This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.

The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.

We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S²ⁿ⁺¹ and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to Eⁿ⁺¹ × Sⁿ(4) in higher dimension.

All results are novel and generalizations of previously obtained results.

In this article, we examine the impact of repeat interactions between VCs and underwriters. Past research has suggested that such interactions build trust and may contribute to more equitable treatment of issuing firms. We adopt an alternative perspective and suggest that these repeat interactions are characterized by reciprocal exchanges facilitated by opportunistic behavior from the VC. Our analysis demonstrates that VCs and underwriters interact in order to appropriate greater value from the IPO. This article provides a more complete understanding of repeat interactions between the VC and the underwriter by identifying characteristics of the relationship that have an impact on the value of the IPO.

The chapter summarizes key literature, including emerging ideas, that is pertinent to the question of how organizations and their leadership deal with and are resilient through crises – highlighting what works in surviving unexpected crises. The chapter presents an illustration of organizational response; it concludes with an analysis of what is missing from the literature and recommends a path forward to expanding actionable knowledge in this area. Multiple, interdependent factors that foster resilience are identified including (1) being sensitive to possible threats – even seemingly small failures, (2) not relying on simple interpretations of events but rather seeking diversity to create a complete view of the environment, (3) leadership that embraces communication, transparency, and continuous learning, (4) valuing expertise and allowing expert staff to make decisions during a crisis, and (5) a cultural commitment to a resiliency mindset that accepts failures as opportunities to learn and improve. Emerging concepts that may foster resilience but require more research include managing paradox, emotional ambivalence and diversity. Additional areas for fruitful research include: the impact of short-term versus long-term, or successive, crises; external versus internal shocks and the framing of the source of shocks; how crisis affect the pace of innovation and change; the role of diversity in organizational responses to crises; and a set of methodological opportunities to leverage natural experiments or simulations in ways that allow for longitudinal data illuminating the full cycle of crises across organizations from anticipation, to response, to longer-term adaptation to the new normal.