TL;DR
This paper reviews fundamental concepts of real and complex smooth vector bundles, emphasizing the notion of tensor fields within the bundle framework rather than just on manifolds.
Contribution
It provides a comprehensive overview of vector bundle theory and introduces tensor fields in the context of smooth bundles, expanding traditional manifold-focused approaches.
Findings
Clarifies the structure of smooth vector bundles
Extends tensor field concepts to bundle frameworks
Serves as a foundational review for further research
Abstract
This is a review of the basic concepts of the theory of real and complex smooth vector bundles with finite rank. Besides, the concept of a tensor field is studied within the general framework of a smooth vector bundle rather than a smooth manifold.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Algebraic Geometry and Number Theory