MANIFOLD TUSHUNCHASI VA ULARNING XOSSALARI
Keywords:
Manifol’d, differensial geometriya, topologiya, tangent fazo, metrik tensor, geodezik, egrilik, atlas, koordinatalar, fazo-vaqt, topologik invariantlar, 3D modellashtirishAbstract
Ushbu maqolada manifol’d tushunchasi, uning differensial geometriya va topologiyadagi o‘rni, asosiy matematik tuzilmalari hamda xossalari keng va chuqur ilmiy yondashuv asosida tahlil qilinadi. Manifol’dlar murakkab fazoviy obyektlarni lokal ravishda Evklid fazosiga o‘xshash ko‘rinishda ifodalash imkonini beruvchi fundamental matematik strukturalar hisoblanadi. Maqolada manifoldlarning koordinatalar tizimi, atlas, tangent fazo, metrik struktura, geodeziklar, kovariant hosila va egrilik kabi tushunchalari batafsil yoritiladi. Shuningdek, ularning robototexnika, kompyuter grafikasi, sun’iy intellekt, mashina o‘rganish va nazariy fizikadagi amaliy qo‘llanilishi ilmiy asosda tahlil qilinadi.References
John M. Lee -Introduction to Smooth Manifolds. Springer, 2013.
James R. Munkres -Topology. Prentice Hall, 2000.
Barrett O’Neill -Elementary Differential Geometry. Academic Press, 2006.
Spivak M. -A Comprehensive Introduction to Differential Geometry. Publish or Perish, 1999.
Do Carmo M.P. -Differential Geometry of Curves and Surfaces. Prentice Hall, 1976.
Nakahara M. -Geometry, Topology and Physics. Taylor & Francis, 2003.
O‘zbek va rus tilidagi adabiyotlar:
Published
2026-05-06
How to Cite
Saliyeva Sevara Ma’mirbek qizi, & Mamatqulova O’g’iloy Quyoshbek qizi. (2026). MANIFOLD TUSHUNCHASI VA ULARNING XOSSALARI. SAMARALI TA’LIM VA BARQAROR INNOVATSIYALAR JURNALI, 4(5), 65–68. Retrieved from https://innovativepublication.uz/index.php/jelsi/article/view/5793
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