Treatise on Differential Geometry and its role in Relativity Theory

TL;DR

This lecture note introduces differential geometry concepts with modern terminology, emphasizing their application to relativity theory, aimed at students in physics and mathematics for educational purposes.

Contribution

It provides an accessible introduction to differential geometry with a focus on its relevance and application to relativity theory for students.

Findings

Differential geometry concepts are explained with modern terminology.

The note demonstrates the applicability of differential geometry to relativity.

Educational problems are included to aid student understanding.

Abstract

This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book with the motivation of geometrical or pictorial way of thinking. This note is an effort of teaching differential geometry and shows its wide applicability to relativity theory. The problems in this lecture note may be useful to the students