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Daniel Waters
Daniel Waters
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I've been self studying differential geometry for a little while now (4-6 months). I am learning from Lee's Introduction to Smooth Manifolds, and I just don't quite get the point of the subject. Why do we study the constructions that we study, such as differential forms, submanifolds, vector bundles, etc. ? What is the goal of differential geometry, i.e., what is the motivation for studying it?

Edit: As Will Sawin suggested, I will describe things I find motivating. I find beautiful structures, unsolved problems, and a general goal of what we are trying to do in the subject to be motivating. For instance, the motivation in topology (point-set) is to find topological invariants of a given space. This leads us to connectedness, compactness, the fundamental group, etc. In this example, we have a general rule for what we are trying to accomplish. What is this such rule in differential geometry?

I've been self studying differential geometry for a little while now (4-6 months). I am learning from Lee's Introduction to Smooth Manifolds, and I just don't quite get the point of the subject. Why do we study the constructions that we study, such as differential forms, submanifolds, vector bundles, etc. ? What is the goal of differential geometry, i.e., what is the motivation for studying it?

I've been self studying differential geometry for a little while now (4-6 months). I am learning from Lee's Introduction to Smooth Manifolds, and I just don't quite get the point of the subject. Why do we study the constructions that we study, such as differential forms, submanifolds, vector bundles, etc. ? What is the goal of differential geometry, i.e., what is the motivation for studying it?

Edit: As Will Sawin suggested, I will describe things I find motivating. I find beautiful structures, unsolved problems, and a general goal of what we are trying to do in the subject to be motivating. For instance, the motivation in topology (point-set) is to find topological invariants of a given space. This leads us to connectedness, compactness, the fundamental group, etc. In this example, we have a general rule for what we are trying to accomplish. What is this such rule in differential geometry?

Source Link
Daniel Waters
Daniel Waters
  • 349
  • 2
  • 11

What's the point of differential geometry?

I've been self studying differential geometry for a little while now (4-6 months). I am learning from Lee's Introduction to Smooth Manifolds, and I just don't quite get the point of the subject. Why do we study the constructions that we study, such as differential forms, submanifolds, vector bundles, etc. ? What is the goal of differential geometry, i.e., what is the motivation for studying it?