يناقش موضوع الرسالة هندسة الفضاءات الجزئية من فضاءات ريمان وهو عمل اعد لنيل درجة الماجستير في الرياضيات .
تقع دراستنا هذه في ثلاثة فصول تتضمن دراسة مرجعية ومن ثم دراسة مسألة الغمر وهندسة الفضاءات الجزئية من فضاءات ريمان .
The thesis topic discusses the geometry of subspaces of Riemann spaces, and it is a work prepared for obtaining a master's degree in mathematics.
Our study falls into three chapters that include a reference study and then a study of the immersion issue and the geometry of subspaces from Riemann spaces.
References used
Luther pfahler eisenhart , riemannian geometry , Princeton University (1949)
In this paper, we define tensors and space Riemann spaces and
fixed curvature, and offer a study of some cases associated
with the search topic, the basic function is to study the
relationships that remain valid when the coordinates system
change to another system.
We prove that the sum A + B of closed subspaces A and B of the inverse
limit of finite dimensional vector spaces, V = limVn (n ∈ N) over an
algebraically closed field of characteristic 0 is closed.
We extend also the basic fact that every ideal of a finite dimensional
semisimple Lie algebra has a unique complement to the case of closed ideals of
prosemisimple Lie algebras.
in this paper we:
defined Riemannian spaces, conformal mappings, Einstein
spaces, Riemannian symmetric spaces, Ricci spaces and
Ricci symmetric spaces, recall the fundamental properties of
these spaces
It is often useful to replace a function with a sequence of smooth functions
approximating the given function to resolve minimizing optimization problems.
The most famous one is the Moreau envelope. Recently the function was organized
using the Br
It is widely accepted that fine-tuning pre-trained language models usually brings about performance improvements in downstream tasks. However, there are limited studies on the reasons behind this effectiveness, particularly from the viewpoint of stru