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      • The Classical Theory of Fields
        • Chapter 1: The Principle of Relativity
          • § 1. Velocity of propagation of interaction
          • § 2. Intervals
          • § 3. Proper time
          • § 4. The Lorentz transformation
          • § 5. Transformation of velocities
          • § 6. Four-vectors
        • Chapter 0: Prefaces, Notation, etc.
          • Table of Contents
          • Prefaces
          • Publisher's Note
          • Notation
      • Blogs
        • Codeforces Round 995 Problem G
        • Transformer
        • Natural Language Processing
        • Binary indexed tree
        • Image to image translation
        • Segment Tree
        • Readme
      • About
      • Codeforces
        • Codeforces Round 1034 (Div. 3)
          • E. MEX Count
          • F. Minimize Fixed Points
          • G. Modular Sorting
        • Codeforces Round 1035 (Div. 2)
          • A. Add or XOR
          • B. Line Segments
          • C. A Good Problem
          • D. Token Removing
          • E. And Constraint
        • Codeforces Round 1037 (Div. 3)
          • F. 1-1-1, Free Tree!
          • G1. Big Wins! (easy version)
          • G2. Big Wins! (hard version)
        • Codeforces Round 1039 (Div. 2)
          • A. Recycling Center
          • B. Deque Process
          • D. Sum of LDS
          • E1. Submedians (Easy Version)
          • E2. Submedians (Hard Version)
        • Codeforces Round 1049 (Div. 2)
          • A. Shift Sort
          • B. Another Divisibility Problem
          • C. Ultimate Value
          • D. A Cruel Segment's Thesis
          • E. Prime Gaming
        • Codeforces Round 1054 (Div. 3)
          • A. Be Positive
          • B. Unconventional Pairs
          • C. MEX Rose
          • D. A and B
          • E. Hidden Knowledge of the Ancients
        • Codeforces Round 1056 (Div. 2)
          • A. El fucho
          • B. Abraham's Great Escape
          • C. The Ancient Wizards' Capes
          • D. Batteries
          • E. Mimo & Yuyu
        • Codeforces Round 1057 (Div. 2)
          • A. Circle of Apple Trees
          • B. Bitwise Reversion
          • C. Symmetrical Polygons
          • D. Not Alone
        • Codeforces Round 1059 (Div. 3)
          • A. Beautiful Average
          • B. Beautiful String
          • C. Beautiful XOR
          • D. Beautiful Permutation
          • E. Beautiful Palindromes
          • F. Beautiful Intervals
          • G. Beautiful Tree
        • Educational Codeforces Round 180 (Rated for Div. 2)
          • A. Race
          • B. Shrinking Array
          • C. Coloring Game
          • D. Reachability and Tree
          • E. Tree Colorings
      • Kangni (Connie) Liu
      • LeetCode
        • LeetCode Contest 469
          • 3697. Compute Decimal Representation
          • 3698. Split Array With Minimum Difference
          • 3699. Number of ZigZag Arrays I
          • 3700. Number of ZigZag Arrays II
      • Riemannian Geometry
        • Chapter 0: Differentiable Manifolds
          • Table of Contents
          • 01 Introduction
          • 02 Differentiable Manifolds Tangent Space
          • 03 Immersions Embeddings Tangent Bundle Orientation
          • 04 Other Examples of Manifolds Orientation
          • 05 Vector Fields Brackets Topology of Manifolds
        • Table of Contents
      • Rudin's Real and Complex Analysis
        • Table of Contents
        • Chapter 1: Abstract Integration
          • 00 Introduction
          • 01 Set Theoretic Notations and Terminology
          • 02 the Concept of Measurability
          • 03 Simple Functions
          • 04 Elementary Properties of Measures
          • 05 Arithmetic in 0 Infinity
          • 06 Integration of Positive Functions
          • 07 Integration of Complex Functions
          • 08 the Role Played by Sets of Measure Zero
          • 09 Exercises
        • Chapter 2: Positive Borel Measures
          • 00 Introduction
          • 01 Vector Spaces
          • 02 Topological Preliminaries
          • 03 the Riesz Representation Theorem
          • 04 Regularity Properties of Borel Measures
          • 05 Lebesgue Measure
          • 06 Continuity Properties of Measurable Functions
          • 07 Exercises
      • Yanan Gong
      • Chapter 0: Differentiable Manifolds
        • 01 Introduction
        • 02 Differentiable Manifolds Tangent Space
        • 03 Immersions Embeddings Tangent Bundle Orientation
        • 04 Other Examples of Manifolds Orientation
        • 05 Vector Fields Brackets Topology of Manifolds
      • Table of Contents
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      Chapter 0: Differentiable Manifolds

      Table of Contents

      • Section 1: Introduction
      • Section 2: Differentiable Manifolds and Tangent Space
      • Section 3: Immersions, Embeddings, Tangent Bundle and Orientation
      • Section 4: Other Examples of Manifolds and Orientation
      • Section 5: Vector fields; brackets. Topology of manifolds