Kuan L. The First Adventures on Differential Geometry 2024

Textbook in PDF format

This book serves as a friendly stepping stone for readers who wish to start learning differential geometry. It lays down the most essential foundations, ensuring that readers feel prepared to tackle more advanced concepts in the future. Differential geometry is often perceived or presented as a myriad of seemingly disjointed ideas to beginners. This book bridges those gaps by following the story of a character named Beng, along with his friends, as they journey to master differential geometry. Starting with the basics in Euclidean space, the book offers an accessible entry point into understanding geometry. It then progresses to curved surfaces and intrinsic geometry, culminating in a quintessential application of Ricci curvature. Readers will explore the Einstein equation and work through the Schwarzschild solution, ultimately calculating the event horizon for a non-rotating black hole