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1 – 10 of 65H. Aruna Kumara, V. Venkatesha and Devaraja Mallesha Naik
Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance…
Abstract
Purpose
Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds.
Design/methodology/approach
The paper opted the tensor calculus on manifolds to find the solution of the CPE.
Findings
In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting.
Originality/value
The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.
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Mohan Khatri and Jay Prakash Singh
This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.
Abstract
Purpose
This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.
Design/methodology/approach
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.
Findings
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.
Originality/value
All results are novel and generalizations of previously obtained results.
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H.M. Manjunatha, S.K. Narasimhamurthy and Zohreh Nekouee
The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.
Abstract
Purpose
The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.
Design/methodology/approach
This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.
Findings
The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.
Originality/value
The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal
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Sudhakar Kumar Chaubey and Uday Chand De
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the…
Abstract
Purpose
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly
Design/methodology/approach
The authors have used the tensorial approach to achieve the goal.
Findings
A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.
Originality/value
The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.
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Doug Paxton and Suzanne Van Stralen
“We live at a hinge time in history, a threshold time when societies and cultures are being recomposed. We are learning that the way life used to work—or the way we thought it…
Abstract
“We live at a hinge time in history, a threshold time when societies and cultures are being recomposed. We are learning that the way life used to work—or the way we thought it should— doesn’t work any longer” (Parks, 2009, p. xv). This article is about learning, culture change, practice and leadership. Many wise minds have articulated the leadership mindset we need for the future, and what remains stubbornly elusive is how we get there. We believe the difficult challenge of developing a new mindset--a new view of the world--to address the complexity and dynamic nature of the 21st century is of central importance to leadership education today. As Einstein famously conveyed, we cannot address the problems of today with the same mindset that created those problems. Our inquiry explores the following questions: “How do we develop the skills, capacities and consciousness necessary for bringing creativity, innovation and a new mindset to our most strategic and pressing organizational challenges? How do we practice our way into a new paradigm of leadership?” We invite you to join us in this inquiry into leadership
This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political…
Abstract
Purpose
This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature.
Design/methodology/approach
The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics).
Findings
The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation.
Research limitations/implications
The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts.
Practical implications
Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies.
Social implications
Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society.
Originality/value
Application of the quantum-like model of Fröhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and Internet-based sources.
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In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for…
Abstract
In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, the equality case is also discussed. By the application of derived inequality, we compute an expression for Dirichlet energy of the involved warping function. Finally, we also proved some classifications for these warped product submanifolds in terms of Ricci solitons and Ricci curvature. A non-trivial example of these warped product submanifolds is provided.
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With increasing acceptance of followership as a counterpart of leadership, the study of followership within graduate-level leadership and business curricula should be equally…
Abstract
With increasing acceptance of followership as a counterpart of leadership, the study of followership within graduate-level leadership and business curricula should be equally considered. Further, an understanding of andragogy, or adult education theory, is of benefit with the inclusion of creativity within a followership curriculum. By developing creative capacity within followership education, graduate students are better equipped to influence the business world with innovative thinking skills that enhance problem solving in an increasingly competitive work environment.
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Gino Cattani, Simone Ferriani, Frédéric Godart and Stoyan V. Sgourev
W. Marcus Lambert, Nanda Nana, Suwaiba Afonja, Ahsan Saeed, Avelino C. Amado and Linnie M. Golightly
Structural mentoring barriers are policies, practices and cultural norms that collectively disadvantage marginalized groups and perpetuate disparities in mentoring. This study…
Abstract
Purpose
Structural mentoring barriers are policies, practices and cultural norms that collectively disadvantage marginalized groups and perpetuate disparities in mentoring. This study aims to better understand structural mentoring barriers at the postdoctoral training stage, which has a direct impact on faculty diversity and national efforts to retain underrepresented groups in research careers.
Design/methodology/approach
A diverse sample of postdoctoral scholars (“postdocs”) from across the USA were asked to participate in focus groups to discuss their training experiences. The authors conducted five 90-min focus groups with 32 biomedical postdocs, including 20 (63%) women and 15 (47%) individuals from underrepresented racial/ethnic groups (URG).
Findings
A social-ecological framework was used to categorize both the upstream and downstream manifestations of structural mentoring barriers, as well as mentoring barriers, overall. Notable structural barriers included: academic politics and scientific hierarchy; inequalities resulting from mentor prestige; the (over) reliance on one mentor; the lack of formal training for academic and non-academic careers; and the lack of institutional diversity and institutional mentor training. To overcome these barriers, postdocs strongly encouraged developing a network or team of mentors and recommended institutional interventions that create more comprehensive professional development, mentorship and belonging.
Originality/value
For postdoctoral scientists, structural mentoring barriers can permeate down to institutional, interpersonal and individual levels, impeding a successful transition to an independent research career. This work provides strong evidence for promoting mentorship networks and cultivating a “mentoring milieu” that fosters a supportive community and a strong culture of mentorship at all levels.
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