Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to ...Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.展开更多
UNESCO,the UN nodal agency for education,science,culture and architecture,has made sustainability a key topic in its development oriented activities,and has launched a new initiative to address the increasing concern ...UNESCO,the UN nodal agency for education,science,culture and architecture,has made sustainability a key topic in its development oriented activities,and has launched a new initiative to address the increasing concern of nonsustainable urbanization which currently occurs in the Asia and Pacific region.It is a region of rapid change,cultural alienation and environmental crisis,with a threatening divide between city and countryside.This paper informs about the interdisciplinary research activities conducted by the newly established UNESCO Chair in Sustainable Urban Development for Asia and the Pacific.The Chair’s roadmap for the next ten years to facilitate sustainable urban growth is explored and described in detail.展开更多
基金supported by NSFC(Grant Nos.12371195,12022111)the Fundamental Research Funds for the Central Universities(Grant No.2042023kf0207)+1 种基金the second author was partially supported by NSFC(Grant No.11831009)Fundings of Innovating Activities in Science and Technology of Hubei Province。
文摘Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.
文摘UNESCO,the UN nodal agency for education,science,culture and architecture,has made sustainability a key topic in its development oriented activities,and has launched a new initiative to address the increasing concern of nonsustainable urbanization which currently occurs in the Asia and Pacific region.It is a region of rapid change,cultural alienation and environmental crisis,with a threatening divide between city and countryside.This paper informs about the interdisciplinary research activities conducted by the newly established UNESCO Chair in Sustainable Urban Development for Asia and the Pacific.The Chair’s roadmap for the next ten years to facilitate sustainable urban growth is explored and described in detail.
