Geodesics generalize the concept of a "straight line" to curved spaces. The book provides rigorous proofs showing that geodesics are the paths of shortest distance between two points on a surface. It covers the differential equations governing geodesics and specific cases like geodesics on spheres, cones, and cylinders. 5. Introduction to Tensors and Riemannian Geometry
Krishna Publication partners with . You can buy the official e-book for roughly ₹150–₹300 ($2–$4 USD). This is a legal PDF with high-resolution diagrams and unlimited downloads.
Written specifically to meet the requirements of Honour's and postgraduate classes. Detailed Syllabus Coverage (Krishna Publication) The book generally covers the following core areas:
For aspirants of the , Differential Geometry and Tensor Analysis hold significant weight. Why UPSC Aspirants Prefer Krishna Series:
: Understanding the shortest paths on curved surfaces. differential geometry krishna publication pdf
Specificity: High (searching for a specific book)
Before exams, the MCQ section at the back of the Krishna publication PDF is gold. It covers quick facts (e.g., "The curvature of a straight line is ___" → Zero).
If you need specific help with a chapter, or perhaps help calculating a Curvature or Torsion formula, please ask!
Authored by K.S. Amur, D.J. Shetty, and C.S. Bagewadi, this text is often the recommended starting point for modern differential geometry at the master's level. It focuses on the concept of —a foundational idea for modern physics and advanced geometry. Geodesics generalize the concept of a "straight line"
The book is written in a standard "textbook + question bank" hybrid style. It is heavy on solved examples and previous year's university exam questions. If you need rigorous proofs and abstract manifold theory (like Do Carmo), this isn’t that book. If you need to pass an Indian university exam next week, this is your book.
The book uses specific vector notation (e.g., $\vecr$, $\dot\vecr$, $\ddot\vecr$). Ensure you understand the difference between derivatives w.r.t arc length ($'$) and w.r.t parameter ($\dot{}$).
It is recommended to check the official Krishna Prakashan website for legitimate digital versions.
Space curves, Serret-Frenet formulas, and curvature/torsion. This is a legal PDF with high-resolution diagrams
Curvature (how a curve bends) and torsion (how a curve twists).
While a free PDF for these titles is not legally available online, here are the best ways to access the material:
Krishna Publication is renowned for its affordable and comprehensive "Krishna Series" maths books. The differential geometry volume is specifically designed to bridge the gap between elementary calculus and advanced geometry.
The paperback editions of the Krishna Series are priced economically for students and are widely available across major e-commerce platforms and local university book stalls. Open-Source Alternatives