How Long to Read Vector Fields on Manifolds

How Long Does it Take to Read Vector Fields on Manifolds?

It takes the average reader and 30 minutes to read Vector Fields on Manifolds by Michael Francis Atiyah

Assuming a reading speed of 250 words per minute. Learn more

Description

This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and...

How long is Vector Fields on Manifolds?

Vector Fields on Manifolds by Michael Francis Atiyah is 30 pages long, and a total of 7,500 words.

This makes it 10% the length of the average book. It also has 9% more words than the average book.

How Long Does it Take to Read Vector Fields on Manifolds Aloud?

The average oral reading speed is 183 words per minute. This means it takes and 40 minutes to read Vector Fields on Manifolds aloud.

What Reading Level is Vector Fields on Manifolds?

Vector Fields on Manifolds is suitable for students ages 8 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Vector Fields on Manifolds?

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