QATLAMALI KO‘PXILLIKLAR TOPOLOGIK AKSLANTIRISHLARI GRUPPASINING XOSSALARI HAQIDA
Keywords:
silliq ko‘pxillik, qatlama, qatlamali ko‘pxillik, topologik akslantirish, topologik gruppa, Xausdorf fazo, kompakt ochiq topologiya, F-kompakt ochiq topologiya.Abstract
Differensial geometriya va topologiyaning zamonaviy yo‘nalishlaridan biri bo‘lgan qatlamali ko‘pxilliklar nazariyasi XX asrning ikkinchi yarmida differensial tenglamalar, differensial geometriya va differensial topologiya fanlarining tutash sohasida paydo bo‘lgan. Ushbu ishda qatlamali ko‘pxilliklar topologik akslantirishlari gruppasining xossalari o‘rganilgan. Xususan, bu gruppaning kompakt ochiq topologiyaga nisbatan toplogik gruppa ekanligi isbotlangan. Bundan tashqari qatlamali ko‘pxilliklar topologik akslantirishlari to ‘plamini sanoqli bazaga ega Xausdorf fazosi ekanligi isbotlangan.
References
C. Ehresmann, Structures feuilletees // Proc. Fifth Canad. Math. Congress. – 1961. – P.109-172.
G. Reeb, Sur certains proprietes topoloiques des varietes feuilletees// Actualite Sci. Indust. 1183 – Paris: Hermann, – 1952.
Molino P. Riemannian foliations // Progress in Mathematics Vol. 73, – Birkhäuser Boston Inc. – 1988. – P.399.
A. Haefliger, Varietes feuilletees // Ann. Scuola Norm. Sup. Pisa. – 1962. – V.16. – P.367-397.
R. Langevin, A list of questions about foliation. Differential topology, foliations group actions // Contemporary Math. – 1994. – V.161. – P.59-80.
Narmanov A.Ya., Sharipov A.S. On the group of foliation isometries// Methods of functional Analysis and topology, Kiev, Ukraine, – 2009. – V.15. – P.195-200.
G.M.Abdishukurova and A.Ya. Narmanov Diffeomorphisms of foliated manifolds // Methods of functional Analysis and topology, Kiev, Ukraine, – 2021. – V.27(2021), no 1, pp.1-9.
Narmanov A.Ya., Sharipov A.S. Geometry of Foliated Manifolds// Extracta mathematicae vol. 31. Num. 2, 2016, pp. 189-197.
A. Narmanov and S. Saitova, On the geometry of orbits of killing vector fields, Differential Equations 50 (2014), 1582–1589.
