George Washington University Differential Geometry Smooth Mapping Practice


Please solve the Question and show all the steps. you may need the note(pdf) but you cannot copy from it

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

In the questions below you need to justify your answers rigorously.
(i) Let 0 :RRM be a smooth map. Define the term singular point of a map
0. Give an example of a map 0 : R + R that has a unique singular point.
(ii) Can a diffeomorphism D : R2 + R2 have singular points?
(ii) Give an example of a smooth map 0 : R2 + R2 whose only singular point is
(iv) Give an example of a non-constant smooth map 0 : R² + R2 such that every
point (2,4) € R2 is singular.
(v) Give an example of a smooth map Ø : R2 + R2 such that the set of its
singular points is the parabola {(x,y) € R2 : y = 2²}.
(i) Let 0 : R4 + R2 be a smooth map of the form,
(21, 12, 13, 14) = (x122 +2314, f(x1, 22, 23, 24)),
where f is an unspecified smooth function. Find a function f : R4 + R
such that the map and the pre-image 0-1(1, 2) satisfy the conditions of the
Regular Value Theorem. Verify that your answer satisfies these conditions.
(ii) Choose any point pe 0-1(1, 2) in your answer for (b)(i). Write down its
coordinates and construct a basis for the tangent space TΣ, where Σ =
0-1(1,2). Justify your answer.

Purchase answer to see full

singular points

Differential geometry

singular point

smooth mapping

minimun dimensions

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.

Peter M.
Peter M.
So far so good! It's safe and legit. My paper was finished on time...very excited!
Sean O.N.
Sean O.N.
Experience was easy, prompt and timely. Awesome first experience with a site like this. Worked out well.Thank you.
Angela M.J.
Angela M.J.
Good easy. I like the bidding because you can choose the writer and read reviews from other students
Lee Y.
Lee Y.
My writer had to change some ideas that she misunderstood. She was really nice and kind.
Kelvin J.
Kelvin J.
I have used other writing websites and this by far as been way better thus far! =)
Antony B.
Antony B.
I received an, "A". Definitely will reach out to her again and I highly recommend her. Thank you very much.
Khadija P.
Khadija P.
I have been searching for a custom book report help services for a while, and finally, I found the best of the best.
Regina Smith
Regina Smith
So amazed at how quickly they did my work!! very happy♥.