In linear algebra, a one-form on a vector space is the same as a linear functional on the space. The usage of one-form in this context usually distinguishes the one-forms from higher-degree multilinear functionals on the space. For details, see linear functional.
In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold


{\displaystyle M}
is a smooth mapping of the total space of the tangent bundle of


{\displaystyle M}


{\displaystyle \mathbb {R} }
whose restriction to each fibre is a linear functional on the tangent space. Symbolically,




{\displaystyle \alpha _{x}}
is linear.
Often one-forms are described locally, particularly in local coordinates. In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates:

where the



{\displaystyle f_{i}}
are smooth functions. From this perspective, a one-form has a covariant transformation law on passing from one coordinate system to another. Thus a one-form is an order 1 covariant tensor field.

View More On
  1. Bandook

    No Submitted ATF Form 1 after successful submission

    Never mind: Found it - need to go through the main ATF website.
  2. pacmanwa

    I laughed at 24 inches, anyone else laugh at the SBR length they put on their Form 1?

    Finally finished picking out parts for my wife's SBR. The final estimated length of the rifle when complete is... 24 inches. I pulled a tape measure out to that length, shouldered it and came out of my office to show her. "Honey look!" *snicker* "This is how big yours's is going to be!" *WHEEZE*...

    Updates from ATF and FBI

    I just called the ATF and quizzed them about the time it takes to get a form 1 through, and they said that the FBI is taking around 60 days from the time the FBI recieves the fingerprint cards, to release of background check. May be shorter, but probably not. I have had a form 1 under review...
  4. Aero Denezol

    NFA/SBR Engraving in Salem?

    Who does this type of work in the Mid-Willamette Valley? I know everyone likes BYE in Portland but I'm hoping to avoid traffic and gasoline by keeping it local. Many thanks in advance.
  5. 1775usmc

    Form 1 approved.

    Form 1 approved in a total of 13 business days. Who knew the government could work that fast..... I mean they already had my money, I was expecting them to take all the time they didn’t truly need.
  6. papersoldier

    Correct / acceptable baffle & endcap hole diameter.

    Just have a quick question for those here experienced with building form 1 suppressors, specifically in 9mm: Is a 3/8" (.375) baffle and endcap hole diameter adequete for 9mm projectiles (assuming the threads on the firearm are perfectly concentric to the bore), or is that cutting it too close...
  7. DownRangeDuck

    eFile Form 1, Trust, Suppressor: Tax stamp question

    eFile Form 1, Trust, Suppressor 12-26-2019: eFiled ATF Form 1, paid with credit card online. 12-27-2019: Mailed fingerprint cards to ATF 12-31-2019: ATF received fingerprint cards 01-06-2020: Inquired about status online via Ask the Experts. ATF replied “Everything required has been received...
  8. CountryGent

    If the Hughes Amendment ceased to exist, what would you Form 1 MG-wise?

    Let's pretend for a moment that the Hughes Amendment is repealed or declared unconstitutional (shaaa ... it could happen). What would you stamp/convert and why? Enjoy!
  9. Build Thread  Another Form 1 - eFile

    Started and sent off an eFile Form 1 this morning. Planning on an all titanium .30 cal can. Since the eFiles are coming in so quick right now, I should have it all back by the time I'm home from a vacation. Thanks for the inspiration @Tomahawk67. Looking to setup a 9.7" Titanium housing...
  10. Tomahawk67

    Form 1 Titanium can

    Just got my Form 1 can approved. Efile took 30 days , now it's time to make some chips.. .
  11. CountryGent

    Anyone use eForms Recently?

    So, I have another Form 1 project (SBR) under works. I'm planning on having the threading and action work done first while it is still Title I. Then I will file for the stamp. I plan on using eForms since it is back now, albeit requiring mailing in fingerprint cards. (There are only two...
  12. O

    Lower for my SBR

    I am hoping someone on here has some experience with this question because I cannot find a good answer. I have a 300BLK pistol I recently built and have never fired. I am rethinking the pistol portion and want to do an SBR. Can I use the same lower from my pistol build and use that for my form...
  13. CountryGent

    New Mailing Address for NFA Forms

    Just a heads up that there is a new mailing address in Oregon for NFA forms 1 and 4. The American Suppressor Association has information here. Updated forms are available for download here. Cheers. National Firearms Act Division P.O. Box 5015 Portland, OR 97208-5015
  14. Wombat of Doom

    Determining length on an SBR for form 1.

    With an AR buffer tube and a collapsible stock, is it from the end of barrel sans barrel device with the stock extended fully? Or to the end of the buffer tube. If you are 1/4 inch off or so because you didn't actually put it together before you had permission, does anyone care or check? I want...
  15. jon321

    Form 1 filed last week what's average wait time?

    All excited about my first Form 1 suppressor purchase just curious on what the typical wait times are. Thanks
  16. jbett98

    SBR Form 1 Question

    I recently purchased a pre ban HK MP5 de-milled parts kit that I want to SBR. I already have a family gun trust with multiple tax stamps in it (pre 41F), and I don't want to go through the hassle of processing three responsible persons forms for the family gun trusts trustee's. So, my question...
  17. C

    Engraver near Hillsboro?

    I just got my first form 1 back, and now I'm looking for an engraver. Anyone have recommendations for near Hillsboro or elsewhere in western Washington county?
  18. czgunner

    Form 1 CLEO?

    Hey all, I'm filling out my (trust) form 1 to make an SBR and have a few questions. My address says Woodland (Clark County), but I'm not in city limits. What should I input for my CLEO information? Also, my trust (pre 41) has a myself, my wife and my daughter listed as trustees. What age is now...
Back Top