PARAMETRIK SIRTLAR UCHUN BIRINCHI KVADRATIK FORMA VA UNING INVARIANTLARI
Keywords:
parametrik sirt, birinchi kvadratik forma, differensial geometriya, metrik invariant, E,F,G, yuza elementi, sirt metrikasi, egri chiziq uzunligi, burchak, parametr almashtirish.Abstract
Ushbu maqolada parametrik sirtlar uchun birinchi kvadratik forma va uning invariantlari o‘rganiladi. Natijalarda birinchi kvadratik forma koeffitsiyentlari orqali sirtning metrik strukturasi aniqlanishi, shuningdek, ifodasi yuza elementi va metrik invariant sifatida xizmat qilishi ko‘rsatiladi. Muhokama qismida ushbu forma yordamida sirt ustidagi egri chiziqlar uzunligi, ikki yo‘nalish orasidagi burchak va lokal geometriya tahlil qilinadi. Xulosa sifatida birinchi kvadratik forma parametrik sirtlarning ichki geometriyasini tavsiflovchi asosiy vosita ekanligi asoslanadi.
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